A309213 A007318 + A065941 - A049310.
1, 2, 1, 3, 3, 1, 2, 6, 5, 1, 1, 5, 12, 6, 1, 2, 3, 14, 17, 8, 1, 3, 7, 14, 24, 26, 9, 1, 2, 12, 27, 30, 45, 33, 11, 1, 1, 9, 45, 62, 70, 66, 45, 12, 1, 2, 5, 44, 111, 147, 120, 104, 54, 14, 1, 3, 11, 39, 128, 273, 273, 217, 140, 69, 15, 1, 2, 18, 65, 139, 366, 546, 518, 329, 200, 80, 17, 1
Offset: 0
Examples
First few rows of the triangle are: 1, 2, 1, 3, 3, 1, 2, 6, 5, 1, 1, 5, 12, 6, 1, 2, 3, 14, 17, 8, 1, 3, 7, 14, 24, 26, 9, 1, ...
Links
- Jinyuan Wang, Table of n, a(n) for n = 0..5150
Programs
-
PARI
T007318(n, k) = binomial(n, k); T065941(n, k) = binomial(n - (k+1)\2, k\2); T049310(n, k) = if ((n+k)%2, 0, (-1)^((n+k)/2 + k) * binomial((n+k)/2, k)); T(n, k) = T007318(n, k) + T065941(n, k) - T049310(n, k); \\ Michel Marcus, Apr 28 2014
Extensions
The old definition of A131376 did not match the data, as Michel Marcus pointed out. The definition there has been corrected, keeping the old data. The present sequence uses the old definition with corrected data from Michel Marcus. - N. J. A. Sloane, Aug 09 2019
More terms from Jinyuan Wang, Aug 29 2019
Comments