A131376 Triangle read by rows: T(n,k) = A007318(n,k) + A065941(n,k) - A168561(n,k).
1, 2, 1, 1, 3, 1, 2, 2, 5, 1, 1, 5, 6, 6, 1, 2, 3, 14, 9, 8, 1, 1, 7, 14, 24, 16, 9, 1, 2, 4, 27, 30, 45, 21, 11, 1, 1, 9, 25, 62, 70, 66, 31, 12, 1, 2, 5, 44, 71, 147, 120, 104, 38, 14, 1, 1, 11, 39, 128, 203, 273, 217, 140, 51, 15, 1, 2, 6, 65, 139, 366, 434, 518, 329, 200, 60, 17, 1
Offset: 0
Examples
First few rows of the triangle are: 1; 2, 1; 1, 3, 1; 2, 2, 5, 1; 1, 5, 6, 6, 1; 2, 3, 14, 9, 8, 1; 1, 7, 14, 24, 16, 9, 1; ...
Programs
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Mathematica
Table[Binomial[n, k] + Binomial[n - Floor[(k+1)/2], Floor[k/2]] - If[EvenQ[n+k], Binomial[(n+k)/2, k], 0], {n, 0, 11}, {k, 0, n}] // Flatten (* Amiram Eldar, May 31 2025 *)
Extensions
The old definition of A131376 did not match its data, as Michel Marcus pointed out. The definition has been corrected here, keeping the data. The old definition with corrected data is now A309213. - N. J. A. Sloane, Aug 09 2019
More terms from Amiram Eldar, May 31 2025
Comments