OFFSET
1,2
COMMENTS
a(n)/a(n-1) tends to 4.50466435...an eigenvalue of M and a root to the characteristic polynomial x^3 - 3x^2 - 7x + 1.
LINKS
Title?, Title?
Index entries for linear recurrences with constant coefficients, signature (3,7,-1).
FORMULA
a(n)=3a(n-1)+7a(n-2)-a(n-3) (follows from the minimal polynomial of the matrix M).
G.f. x*(1+3*x) / ( 1-3*x-7*x^2+x^3 ). - R. J. Mathar, Mar 03 2013
EXAMPLE
a(7)=10517 because M^7= [6682,9842,10517;9842,14401,15438;10517,15438,16524].
MAPLE
with(linalg): M[1]:=matrix(3, 3, [0, 2, 1, 2, 1, 2, 1, 2, 2]): for n from 2 to 25 do M[n]:=multiply(M[1], M[n-1]) od: seq(M[n][3, 1], n=1..25);
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson & Roger L. Bagula, Jul 01 2006
EXTENSIONS
Corrected by T. D. Noe, Nov 07 2006
Edited by N. J. A. Sloane, Dec 04 2006
STATUS
approved