A367114 G.f. satisfies A(x) = 1 + 2*x*A(x) + x^4*A(x)^4.

1, 2, 4, 8, 17, 42, 124, 408, 1380, 4616, 15184, 49568, 162518, 539580, 1818184, 6203088, 21339916, 73776024, 255853744, 889678688, 3102779785, 10856555130, 38115293308, 134243564056, 474159194316, 1678926445272, 5957812156144, 21183679310048

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

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

Prog

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

Crossrefs

Cf. A002293, A127902, A190590, A367115.

Sequence in context: A156805 A200542 A272105 * A283162 A364210 A231221

Adjacent sequences: A367111 A367112 A367113 * A367115 A367116 A367117

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 05 2023

Status

approved