OFFSET
0,13
FORMULA
a(n) = first component of v(n) = M^n v(0), where v(0)=[0,0,0,0,0,1] and
M = {{0, 1, 0, 0, 0, 0},
{0, 0, 1, 0, 0, 0},
{0, 0, 0, 1, 0, 0},
{0, 0, 0, 0, 1, 0},
{0, 0, 0, 0, 0, 1},
{-1, 1, 0, 0, 1, 0}}.
MATHEMATICA
M = {{0, 1, 0, 0, 0, 0},
{0, 0, 1, 0, 0, 0},
{0, 0, 0, 1, 0, 0},
{0, 0, 0, 0, 1, 0},
{0, 0, 0, 0, 0, 1},
{-1, 1, 0, 0, 1, 0}};
v[0] = Table[If[n == 6, 1, 0], {n, 1, 6}]
v[n_] := v[n] = M.v[n - 1];
b = Table[v[n][[1]], {n, 0, 50}]
CoefficientList[Series[x^5/((1-x)(1+x-x^5)), {x, 0, 60}], x] (* Harvey P. Dale, May 15 2021 *)
PROG
(Magma) M:=Matrix([[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [-1, 1, 0, 0, 1, 0]]); V:=Matrix([[0], [0], [0], [0], [0], [1]]); [ (M^n*V)[1][1]: n in [0..60] ]; // Klaus Brockhaus, Nov 30 2010
CROSSREFS
KEYWORD
sign,easy,less
AUTHOR
Roger L. Bagula, Nov 28 2010
STATUS
approved