OFFSET
0,2
COMMENTS
Top element of the vector obtained by multiplying the n-th power of the 6 X 6 matrix [[0, 1, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 1, 0]] by the column vector [0, 1, 1, 2, 3, 5].
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,5,0,-4).
FORMULA
From Colin Barker, Sep 09 2016: (Start)
a(n) = -2*(1/6 + (-2)^n/3 + (-1)^n/2 - 2^n).
a(n) = 5*a(n-2)-4*a(n-4) for n>3.
(End)
MATHEMATICA
M = {{0, 1, 0, 0, 0, 1}, {1, 0, 1, 0, 0, 0}, {0, 1, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 0, 1}, {1, 0, 0, 0, 1, 0}} v[1] = {0, 1, 1, 2, 3, 5} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
LinearRecurrence[{0, 5, 0, -4}, {0, 6, 4, 22}, 40] (* Harvey P. Dale, Jul 28 2024 *)
PROG
(PARI) concat(0, Vec(2*x*(3+2*x-4*x^2)/((1-x)*(1+x)*(1-2*x)*(1+2*x)) + O(x^40))) \\ Colin Barker, Sep 09 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula and Gary W. Adamson, Jun 28 2006
STATUS
approved