A392673 a(n) = Sum_{k=0..floor(n/2)} binomial(k+1,3*n-6*k+1).

1, 0, 2, 0, 3, 0, 4, 1, 5, 5, 6, 15, 7, 35, 9, 70, 17, 126, 46, 210, 131, 331, 342, 506, 805, 781, 1730, 1287, 3448, 2366, 6465, 4823, 11562, 10388, 20026, 22509, 34223, 47651, 58976, 97376, 104673, 191710, 193823, 364876, 374077, 675850, 742811, 1229305, 1491735, 2219064

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1,1).

Formula

G.f.: (1-x^2) / ((1-x^2)^3 - x^7).

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) + a(n-7).

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^2)/((1-x^2)^3-x^7))

Crossrefs

Cf. A390035, A392253.

Sequence in context: A239241 A263395 A240139 * A390218 A360952 A008800

Adjacent sequences: A392670 A392671 A392672 * A392674 A392675 A392676

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 19 2026

Status

approved