A108479 Antidiagonal sums of number triangle A086645.

1, 1, 2, 7, 17, 44, 117, 305, 798, 2091, 5473, 14328, 37513, 98209, 257114, 673135, 1762289, 4613732, 12078909, 31622993, 82790070, 216747219, 567451585, 1485607536, 3889371025, 10182505537, 26658145586, 69791931223, 182717648081

Offset: 0

Author

Paul Barry, Jun 04 2005

Keywords

• easy
• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (2,1,2,-1).

Crossrefs

Cf. A005252, A051286, A086645, A182890.

Cf. A381421, A382230, A382470, A382471, A382472, A382473, A382474.

Cf. A376729, A376730, A376731.

Programs

Mathematica

LinearRecurrence[{2,1,2,-1},{1,1,2,7},30] (* Harvey P. Dale, Jun 01 2021 *)

Formula

G.f.: (1 - x - x^2)/(1 - 2*x - x^2 - 2*x^3 + x^4).

a(n) = 2*(n-1) + a(n-2) + 2*a(n-3) - a(n-4).

a(n) = Sum_{k=0..floor(n/2)} C(2*(n-k), 2*k).

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-k} C(2*(n-2*k), j) * C(2*k, j).

a(n) = A005252(2*n). - Seiichi Manyama, Aug 11 2024