A265033 Generating function A(x) satisfies A = 1 + x*A^6 + x^2*A^12.

1, 1, 7, 69, 794, 9976, 132657, 1835406, 26149390, 381047316, 5652729938, 85083226696, 1296149152770, 19946485967765, 309623839343190, 4842246124795062, 76223652657288606, 1206767364167388590, 19202880705976262634, 306959907226679676021, 4926844631755358159974

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..800

Gi-Sang Cheon, S.-T. Jin, L. W. Shapiro, A combinatorial equivalence relation for formal power series, Linear Algebra and its Applications, Available online 30 March 2015.

Formula

See page 11 of Cheon et al. 2015 for an explicit formula for a(n).

a(n) ~ 3^(6*n + 1/4) * (5 + sqrt(69))^(n + 1/2) * (39 + sqrt(69))^(6*n + 3/2) / (23^(1/4) * sqrt(Pi) * n^(3/2) * 2^(n+2) * 11^(12*n + 3)). - Vaclav Kotesovec, Nov 20 2017

Maple

a:= n-> coeff(series(RootOf(A=1+x*A^6+x^2*A^12, A), x, n+1), x, n):
seq(a(n), n=0..30);  # Alois P. Heinz, Dec 09 2015

Mathematica

m = 21; A[_] = 0;
Do[A[x_] = 1 + x A[x]^6 + x^2 A[x]^12 + O[x]^m, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Oct 04 2019 *)

Crossrefs

Sequence in context: A084774 A025757 A243668 * A226270 A121351 A302353

Adjacent sequences: A265030 A265031 A265032 * A265034 A265035 A265036

Keyword

nonn

Author

N. J. A. Sloane, Dec 05 2015

Extensions

More terms from Alois P. Heinz, Dec 09 2015

Status

approved