%I #31 Aug 19 2022 06:22:19
%S 1,1,30,468,7560,121824,1963440,31644432,510008400,8219725776,
%T 132476037840,2135095631568,34411003154640,554596768687824,
%U 8938349587100880,144057985642894032,2321760077211226320,37419444899740487376,603083354885909384400,9719800331483969538768
%N a(n) is the value of the first entry in the matrix A^n where A = [{1,2,3}, {4,5,6}, {7,8,9}].
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (15,18).
%F a(n) = (1/(132*2^n)) * ((55-7*sqrt(33))*(15+3*sqrt(33))^n + (55+7*sqrt(33))*(15-3*sqrt(33))^n).
%F G.f.: (3*x^2 + 14*x - 1)/(18*x^2 + 15*x - 1).
%F 3^n | a(n+1). - _R. J. Mathar_, Jan 09 2020
%F Let b(n)=3^n*A015535(n) = 1,15,243,3915,.. (n>=0). Then 6*a(n) = 5*b(n)-69*b(n-1), n>0. - _R. J. Mathar_, Aug 19 2022
%o (PARI) a(n) = ([1,2,3; 4,5,6; 7,8,9]^n)[1,1]; \\ _Michel Marcus_, Oct 26 2018
%K nonn,easy
%O 0,3
%A _Peter James Foreman_, Oct 26 2018