A352007 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 3^k * a(k) * a(n-2*k-1).

1, 1, 1, 4, 7, 19, 40, 178, 379, 1237, 2941, 10378, 24628, 78928, 198820, 813550, 1971907, 6587245, 16980079, 61488286, 155573011, 515316037, 1363261084, 4937498686, 12796438252, 42078038668, 113153315824, 390012381346, 1036020692356, 3379994401042, 9240830253940

Offset

0,4

Links

Table of n, a(n) for n=0..30.

Formula

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

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[3^k a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 30}]
nmax = 30; A[_] = 0; Do[A[x_] = 1/(1 - x A[3 x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A000621, A015084, A352006, A352008.

Sequence in context: A006130 A140167 A182228 * A182646 A190646 A220011

Adjacent sequences: A352004 A352005 A352006 * A352008 A352009 A352010

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 28 2022

Status

approved