A366588 G.f. A(x) satisfies A(x) = 1 + x^3*(1+x)*A(x)^2.

1, 0, 0, 1, 1, 0, 2, 4, 2, 5, 15, 15, 19, 56, 84, 98, 224, 420, 552, 1002, 2022, 3069, 4983, 9801, 16577, 26455, 49049, 87945, 144287, 255112, 465244, 792012, 1369862, 2482714, 4348838, 7509580, 13439724, 23911044, 41643744, 73832632, 132039816, 232391394

Offset

0,7

Links

Robert Israel, Table of n, a(n) for n = 0..3794

Formula

G.f.: A(x) = 2 / (1+sqrt(1-4*x^3*(1+x))).

a(n) = Sum_{k=0..floor(n/3)} binomial(k,n-3*k) * binomial(2*k,k)/(k+1).

(4*n + 8)*a(n) + (22 + 8*n)*a(n + 1) + (14 + 4*n)*a(n + 2) + (-8 - n)*a(n + 4) + (-8 - n)*a(n + 5) = 0. - Robert Israel, Oct 14 2024

Maple

f:= gfun:-rectoproc({(4*n + 8)*a(n) + (22 + 8*n)*a(n + 1) + (14 + 4*n)*a(n + 2) + (-8 - n)*a(n + 4) + (-8 - n)*a(n + 5) = 0, a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=1}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Oct 14 2024

Prog

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

Crossrefs

Cf. A115178, A366589.

Cf. A248100.

Sequence in context: A120493 A085880 A055883 * A085843 A198715 A216663

Adjacent sequences: A366585 A366586 A366587 * A366589 A366590 A366591

Keyword

nonn

Author

Seiichi Manyama, Oct 14 2023

Status

approved