Need Help in identifying the series

M

mmalam

New member
Joined
Sep 30, 2022
Messages
2
Hi,

I need help identifying the series, which at first looks like exponents of 11.

Here is the series

1,1
1,2,1
1,3,3,1
1,4,6,4,1
1,5,10,10,5,1
1,6,15,20,15,6,1
1,7,21,35,35,21,7,1
1,8,28,56,70,56,28,8,1

As it can be observed that every number set is palindrome, and first four are exactly 11 to the power 1,2,3, and 4.

How I made/generated it:

-> Start from 11.
-> Just copy 1 from above to next series.
-> Take sums of adjacent numbers and put it into next series.
-> Copy the last one in new series.

Example:
-> 1,1 (Starting point)
-> 1 (copied from above), 2 (1+1), 1 (copied last one)
-> 1 (copied from above), 3 (2+1), 3 (1+2), 1 (copied last one)

Didn't started it from any other number yet, as I have been looking for name of this type of series.

Please let me know if you know anything about it, or perhaps a link to guide me.

Thanks in advance.
 
mmalam said:
Hi,

I need help identifying the series, which at first looks like exponents of 11.

Here is the series

1,1
1,2,1
1,3,3,1
1,4,6,4,1
1,5,10,10,5,1
1,6,15,20,15,6,1
1,7,21,35,35,21,7,1
1,8,28,56,70,56,28,8,1

As it can be observed that every number set is palindrome, and first four are exactly 11 to the power 1,2,3, and 4.

How I made/generated it:

-> Start from 11.
-> Just copy 1 from above to next series.
-> Take sums of adjacent numbers and put it into next series.
-> Copy the last one in new series.

Example:
-> 1,1 (Starting point)
-> 1 (copied from above), 2 (1+1), 1 (copied last one)
-> 1 (copied from above), 3 (2+1), 3 (1+2), 1 (copied last one)

Didn't started it from any other number yet, as I have been looking for name of this type of series.

Please let me know if you know anything about it, or perhaps a link to guide me.

Thanks in advance.
Click to expand...
(a + b) =1*a + 1*b

(a + b)2 = 1*a2 + 2*ab + 1*b2

(a + b)3 = 1*a3 + 3*a2b + 3* ab2 + 1*b3

continue........
 
mmalam said:
Hi,

I need help identifying the series, which at first looks like exponents of 11.

Here is the series

1,1
1,2,1
1,3,3,1
1,4,6,4,1
1,5,10,10,5,1
1,6,15,20,15,6,1
1,7,21,35,35,21,7,1
1,8,28,56,70,56,28,8,1

As it can be observed that every number set is palindrome, and first four are exactly 11 to the power 1,2,3, and 4.

How I made/generated it:

-> Start from 11.
-> Just copy 1 from above to next series.
-> Take sums of adjacent numbers and put it into next series.
-> Copy the last one in new series.

Example:
-> 1,1 (Starting point)
-> 1 (copied from above), 2 (1+1), 1 (copied last one)
-> 1 (copied from above), 3 (2+1), 3 (1+2), 1 (copied last one)

Didn't started it from any other number yet, as I have been looking for name of this type of series.

Please let me know if you know anything about it, or perhaps a link to guide me.

Thanks in advance.
Click to expand...
Search for Pascal's Triangle.
 
Thanks for guidance, I will further look into Pascal's triangle and binomial expansion
 
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