A108479 - OEIS

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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

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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