A375320 Expansion of (1 + x)/(1 - x^3*(1 + x)^4).

1, 1, 0, 1, 5, 10, 11, 14, 37, 85, 139, 204, 371, 768, 1432, 2398, 4117, 7685, 14422, 25744, 45037, 80888, 148408, 269402, 480873, 859580, 1554254, 2817518, 5074004, 9103828, 16384908, 29588793, 53381548, 96068570, 172864927, 311535484, 561770980, 1012168575

Offset

0,5

Links

Table of n, a(n) for n=0..37.

Index entries for linear recurrences with constant coefficients, signature (0,0,1,4,6,4,1).

Formula

a(n) = a(n-3) + 4*a(n-4) + 6*a(n-5) + 4*a(n-6) + a(n-7).

a(n) = Sum_{k=0..floor(n/3)} binomial(4*k+1,n-3*k).

a(n) = A375318(n) + A375318(n-1).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec((1+x)/(1-x^3*(1+x)^4))
(PARI) a(n) = sum(k=0, n\3, binomial(4*k+1, n-3*k));

Crossrefs

Cf. A375316, A375318.

Sequence in context: A094016 A116033 A290469 * A140507 A297255 A296699

Adjacent sequences: A375317 A375318 A375319 * A375321 A375322 A375326

Keyword

nonn

Author

Seiichi Manyama, Aug 12 2024

Status

approved