Formula to a sequence of numbers

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mathy24

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Hello,
I am pretty new to this forum. I have read a lot here and it helped me a lot to finish my studies in applied sciences.

I had an interview yesterday and I got a tricky question: What formula is producing the following sequence of numbers:

3,7,21,49,224

I could not answer this question and the guy on the opposite site has not given me a solution afterwards. Did not get the job and I am still struggling to find out the formula.

Any help to crack the questIon?
 
Last edited:
I found this exact same question posted on Mathematica Stack Exchange (possibly by you). It has since been deleted due to being off-topic, having nothing to do with the Mathematica software (If it was you who posted the question, you may have meant to post it to the regular MathematicS Stack Exchange, where the question would most likely not have been deleted). That said, the best advice I can give you is to quote a user who responded to that question before it was deleted. He says:

"Undoubtedly the 'solution' is supposed to be something 'out of the box' to test your 'creative thinking'. Questions like this are very cruel and unfair. I remember once as a boy growing up on the West coast, a teacher gave me a book of puzzles for talented children and it had number sequences. One of the sequences was the intersection of streets on one of the subway lines in Manhattan, as though a child in Los Angeles would somehow know that. People who pose such problems are just complete [***]holes in my opinion."

In the end, it's next to impossible to know what the "correct" answer that your interviewer had in mind was. One possible polynomial which generates this sequence is, assuming that I did not mis-type it:

-673909/1307674368000*x^15 + 5004253/87178291200*x^14 - 151337/52254720*x^13 + 9320029/106444800*x^12 - 25409989753/14370048000*x^11 + 2192506957/87091200*x^10 - 19011117413/73156608*x^9 + 1200887962891/609638400*x^8 - 3585932821063/326592000*x^7 + 647416874047/14515200*x^6 - 18586394742863/143700480*x^5 + 30899291755337/119750400*x^4 - 274137631043849/825552000*x^3 + 36933161067083/151351200*x^2 - 87781079/1155*x + 1

The sequence you gave is generated by plugging in x values from 0 to 7. When x = 8, the polynomial's value is 467.
 
mathy24 said:
Hello,
I am pretty new to this forum. I have read a lot here and it helped me a lot to finish my studies in applied sciences.

I had an interview yesterday and I got a tricky question: What formula is producing the following sequence of numbers:

3,7,21,49,224

I could not answer this question and the guy on the opposite site has not given me a solution afterwards. Did not get the job and I am still struggling to find out the formula.

Any help to crack the questIon?
Click to expand...
Part of the problem with a question like this is that a there is a formula which will give a next number of anything you wish. For example suppose we had a formula P(x) which gave that sequence for, in order, x=0, x=1, x=2, x=3, x=4, x=5, see
http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html
for the The Lagrange interpolating polynomial as an example.

For any give value y6, we can now construct a formula, F(x), such that F(6)=y6. That is, the formula
F(x) = P(x) - P(6) + \(\displaystyle \frac{x\, (x-1)\, (x-2)\, (x-3)\, (x-4)\, (x-5)}{6\, *\, 5\, *\, 4\, *\, 3\, *\, 2\, *\, 1}\, y_6\)
has a value of y6 at x=6. Note that this is only one of many such functions F(x)
 
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ksdhart said:
I found this exact same question posted on Mathematica Stack Exchange (possibly by you). It has since been deleted due to being off-topic, having nothing to do with the Mathematica software (If it was you who posted the question, you may have meant to post it to the regular MathematicS Stack Exchange, where the question would most likely not have been deleted). That said, the best advice I can give you is to quote a user who responded to that question before it was deleted. He says:

"Undoubtedly the 'solution' is supposed to be something 'out of the box' to test your 'creative thinking'. Questions like this are very cruel and unfair. I remember once as a boy growing up on the West coast, a teacher gave me a book of puzzles for talented children and it had number sequences. One of the sequences was the intersection of streets on one of the subway lines in Manhattan, as though a child in Los Angeles would somehow know that. People who pose such problems are just complete [***]holes in my opinion."

In the end, it's next to impossible to know what the "correct" answer that your interviewer had in mind was. One possible polynomial which generates this sequence is, assuming that I did not mis-type it:

-673909/1307674368000*x^15 + 5004253/87178291200*x^14 - 151337/52254720*x^13 + 9320029/106444800*x^12 - 25409989753/14370048000*x^11 + 2192506957/87091200*x^10 - 19011117413/73156608*x^9 + 1200887962891/609638400*x^8 - 3585932821063/326592000*x^7 + 647416874047/14515200*x^6 - 18586394742863/143700480*x^5 + 30899291755337/119750400*x^4 - 274137631043849/825552000*x^3 + 36933161067083/151351200*x^2 - 87781079/1155*x + 1

The sequence you gave is generated by plugging in x values from 0 to 7. When x = 8, the polynomial's value is 467.
Click to expand...

Very interesting, but how did you get those numbers? Like -673909/1307674368000, 5004253/87178291200, 151337/52254720, etc...?
 
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