OFFSET
0,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,9,3,-17,-8,6,7,-1,1).
MATHEMATICA
M = {{0, 1, 0, 1, 0, 0, 0, 0, 0},
{0, 0, 1, 0, 1, 0, 0, 0, 0},
{1, 1, 0, 0, 0, 1, 0, 0, 0},
{1, 0, 0, 0, 0, 1, 1, 0, 0},
{0, 1, 0, 1, 0, 1, 0, 1, 0},
{0, 0, 1, 0, 1, 0, 0, 0, 1},
{0, 0, 0, 1, 0, 0, 0, 1, 0},
{0, 0, 0, 0, 1, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 1, 1, 1, 0}};
v[0]= {0, 0, 0, 0, 0, 0, 0, 0, 1};
v[n_] := v[n] = M.v[n - 1]
Table[v[n][[1]], {n, 0, 30}] (* or *)
LinearRecurrence[{0, 9, 3, -17, -8, 6, 7, -1, 1}, {0, 0, 0, 1, 4, 8, 33, 68, 245}, 31] (* Georg Fischer, May 03 2019 *)
CoefficientList[Series[x^3*(1+4*x-x^2-6*x^3+x^4)/(1-9*x^2-3*x^3+17*x^4 + 8*x^5-6*x^6-7*x^7+x^8-x^9), {x, 0, 30}], x] (* G. C. Greubel, May 03 2019 *)
PROG
(PARI) my(x='x+O('x^30)); concat([0, 0, 0], Vec(x^3*(1+4*x-x^2-6*x^3+x^4)/( 1-9*x^2-3*x^3+17*x^4+8*x^5-6*x^6-7*x^7+x^8-x^9))) \\ G. C. Greubel, May 03 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0, 0, 0] cat Coefficients(R!( x^3*(1+4*x-x^2-6*x^3+x^4)/( 1-9*x^2-3*x^3+17*x^4+8*x^5 -6*x^6-7*x^7+x^8-x^9) )); // G. C. Greubel, May 03 2019
(Sage) (x^3*(1+4*x-x^2-6*x^3+x^4)/( 1-9*x^2-3*x^3 +17*x^4+8*x^5-6*x^6 -7*x^7+x^8-x^9)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 03 2019
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula, Nov 24 2010
EXTENSIONS
Definition corrected by Georg Fischer, May 03 2019
STATUS
approved