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

0,3

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).

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

Mathematica

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

Prog

(Python)
from sympy import fibonacci
def A108479(n): return fibonacci(2*n+1)+(1, 0, -1)[n%3]>>1 # Chai Wah Wu, Jun 11 2026

Crossrefs

Cf. A005252, A051286, A086645, A182890.

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

Cf. A376729, A376730, A376731.

Sequence in context: A393177 A239357 A106910 * A178441 A014742 A367687

Adjacent sequences: A108476 A108477 A108478 * A108480 A108481 A108482

Keyword

easy,nonn

Author

Paul Barry, Jun 04 2005

Status

approved