The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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}]. 0
 1, 1, 30, 468, 7560, 121824, 1963440, 31644432, 510008400, 8219725776, 132476037840, 2135095631568, 34411003154640, 554596768687824, 8938349587100880, 144057985642894032, 2321760077211226320, 37419444899740487376, 603083354885909384400, 9719800331483969538768 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)