|
%I #16 Oct 04 2019 08:47:21
%S 1,1,7,69,794,9976,132657,1835406,26149390,381047316,5652729938,
%T 85083226696,1296149152770,19946485967765,309623839343190,
%U 4842246124795062,76223652657288606,1206767364167388590,19202880705976262634,306959907226679676021,4926844631755358159974
%N Generating function A(x) satisfies A = 1 + x*A^6 + x^2*A^12.
%H Alois P. Heinz, <a href="/A265033/b265033.txt">Table of n, a(n) for n = 0..800</a>
%H Gi-Sang Cheon, S.-T. Jin, L. W. Shapiro, <a href="http://dx.doi.org/10.1016/j.laa.2015.03.015">A combinatorial equivalence relation for formal power series</a>, Linear Algebra and its Applications, Available online 30 March 2015.
%F See page 11 of Cheon et al. 2015 for an explicit formula for a(n).
%F 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
%p a:= n-> coeff(series(RootOf(A=1+x*A^6+x^2*A^12, A), x, n+1), x, n):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Dec 09 2015
%t m = 21; A[_] = 0;
%t Do[A[x_] = 1 + x A[x]^6 + x^2 A[x]^12 + O[x]^m, {m}];
%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 04 2019 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Dec 05 2015
%E More terms from _Alois P. Heinz_, Dec 09 2015
|
