A370722 a(n) = Sum_{k=0..floor(n/7)} binomial(n-4*k,3*k).

1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 21, 36, 57, 85, 122, 173, 249, 371, 575, 918, 1485, 2398, 3830, 6030, 9369, 14422, 22107, 33909, 52226, 80888, 125925, 196706, 307653, 480873, 750275, 1168085, 1815191, 2817518, 4371772, 6785606, 10539893, 16384908, 25488736

Offset

0,8

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

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

Formula

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

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-7).

Mathematica

LinearRecurrence[{3, -3, 1, 0, 0, 0, 1}, Table[1, 7], 50] (* Paolo Xausa, Mar 15 2024 *)

Prog

(PARI) a(n) = sum(k=0, n\7, binomial(n-4*k, 3*k));
(PARI) my(N=50, x='x+O('x^N)); Vec((1-x)^2/((1-x)^3-x^7))

Crossrefs

Cf. A003522, A100134, A137356.

Cf. A003520, A005689, A348289.

Sequence in context: A332063 A050407 A113032 * A100134 A365732 A137356

Adjacent sequences: A370719 A370720 A370721 * A370723 A370724 A370725

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 28 2024

Status

approved