A348879 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(3*x)).

1, 1, 2, 6, 29, 221, 2815, 59607, 2175115, 134785987, 14543011028, 2682224473296, 864129873439979, 476879023670530355, 460188677448639450646, 761220053428592181980874, 2202591080616789155249254723, 10927081698418028875550581480027, 94836180093445711611212497662570806

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

a(n) ~ c * 3^(n*(n-2)/4), where c = 4.2101130581370834571021724998929772199905440992108887037121562184404379... - Vaclav Kotesovec, Nov 03 2021

Mathematica

nmax = 18; A[_] = 0; Do[A[x_] = 1/(1 - x - x^2 A[3 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[3^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 18}]

Crossrefs

Cf. A001006, A015084, A348878, A348880.

Sequence in context: A321961 A088957 A030538 * A326900 A181812 A330648

Adjacent sequences: A348876 A348877 A348878 * A348880 A348881 A348882

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 02 2021

Status

approved