A375362 Expansion of 1/( (1 + x) * (1 - x*(1 + x)^3) ).

1, 0, 4, 6, 20, 49, 132, 344, 908, 2384, 6273, 16492, 43372, 114050, 299916, 788673, 2073944, 5453760, 14341528, 37713312, 99173121, 260791400, 685792228, 1803399102, 4742323108, 12470688497, 32793647356, 86236081272, 226771411940, 596331286320

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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

Formula

a(n) = 4*a(n-2) + 6*a(n-3) + 4*a(n-4) + a(n-5).

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

a(n) = A375363(n) + A375363(n-1).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/((1+x)*(1-x*(1+x)^3)))
(PARI) a(n) = sum(k=0, n, binomial(3*k-1, n-k));

Crossrefs

Cf. A375363.

Sequence in context: A227959 A088015 A374259 * A027377 A048789 A038069

Adjacent sequences: A375359 A375360 A375361 * A375363 A375364 A375365

Keyword

nonn

Author

Seiichi Manyama, Aug 13 2024

Status

approved