A392488 a(n) = Sum_{k=0..floor((2*n+1)/7)} binomial(2*k+1,2*n-7*k+1).

1, 0, 0, 1, 3, 0, 0, 5, 10, 1, 1, 21, 35, 7, 9, 84, 126, 37, 56, 330, 462, 178, 297, 1287, 1717, 820, 1443, 5006, 6452, 3683, 6643, 19464, 24481, 16252, 29512, 75739, 93709, 70737, 127909, 295152, 361590, 304437, 544603, 1152351, 1405418, 1297892, 2288483

Offset

0,5

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,4,0,0,1,-2,1).

Formula

G.f.: (1 + x^3 - x^4) / (1 - 4*x^4 - x^7*(1-x)^2).

a(n) = 4*a(n-4) + a(n-7) - 2*a(n-8) + a(n-9).

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1+x^3-x^4)/(1-4*x^4-x^7*(1-x)^2))

Crossrefs

Cf. A392456.

Sequence in context: A317465 A051174 A273089 * A362021 A330735 A127773

Adjacent sequences: A392485 A392486 A392487 * A392489 A392490 A392491

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 14 2026

Status

approved