A321045 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}].

1, 1, 30, 468, 7560, 121824, 1963440, 31644432, 510008400, 8219725776, 132476037840, 2135095631568, 34411003154640, 554596768687824, 8938349587100880, 144057985642894032, 2321760077211226320, 37419444899740487376, 603083354885909384400, 9719800331483969538768

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (15,18).

Formula

a(n) = (1/(132*2^n)) * ((55-7*sqrt(33))*(15+3*sqrt(33))^n + (55+7*sqrt(33))*(15-3*sqrt(33))^n).

G.f.: (3*x^2 + 14*x - 1)/(18*x^2 + 15*x - 1).

3^n | a(n+1). - R. J. Mathar, Jan 09 2020

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

Prog

(PARI) a(n) = ([1, 2, 3; 4, 5, 6; 7, 8, 9]^n)[1, 1]; \\ Michel Marcus, Oct 26 2018

Crossrefs

Sequence in context: A010982 A022594 A321955 * A004416 A125487 A258417

Adjacent sequences: A321042 A321043 A321044 * A321046 A321047 A321048

Keyword

nonn,easy

Author

Peter James Foreman, Oct 26 2018

Status

approved