A367115 G.f. satisfies A(x) = 1 + 2*x*A(x) + 2*x^4*A(x)^4.

1, 2, 4, 8, 18, 52, 184, 688, 2512, 8864, 30784, 107648, 384432, 1403872, 5205568, 19443328, 72817856, 273199488, 1027939072, 3883718144, 14741042464, 56189409088, 214931447680, 824443822848, 3169934397184, 12214858010112, 47168251137024

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = Sum_{k=0..floor(n/4)} 2^(n-3*k) * binomial(n,4*k) * A002293(k).

Prog

(PARI) a(n) = sum(k=0, n\4, 2^(n-3*k)*binomial(n, 4*k)*binomial(4*k, k)/(3*k+1));

Crossrefs

Cf. A002293, A127902, A190590, A367114.

Cf. A071356, A367113.

Sequence in context: A034766 A099785 A333497 * A166952 A135422 A116723

Adjacent sequences: A367112 A367113 A367114 * A367116 A367117 A367118

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 05 2023

Status

approved