OFFSET
0,8
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,1,-3).
FORMULA
a(n) = 2*a(n-1) + a(n-3) - 3*a(n-4) for n>=4; a(0)=0, a(1)=-1, a(2)=0, a(3)=0.
G.f.: -x^2*(1 - 2*x) / (1 - 2*x - x^3 + 3*x^4). - Colin Barker, Mar 03 2017
MAPLE
a[0]:=0: a[1]:=0: a[2]:=-1: a[3]:=0: for n from 4 to 42 do a[n]:=2*a[n-1]+a[n-3]-3*a[n-4] od: seq(a[n], n=0..42);
MATHEMATICA
M = {{0, -1, 1, 0}, {0, 0, -1, 1}, {1, 1, 1, 0}, {0, 1, 1, 1}}; v[1] = {0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
PROG
(PARI) concat(vector(2), Vec(-x^2*(1 - 2*x) / (1 - 2*x - x^3 + 3*x^4) + O(x^50))) \\ Colin Barker, Mar 03 2017
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Gary W. Adamson and Roger L. Bagula, Oct 20 2006
EXTENSIONS
Edited by N. J. A. Sloane, Oct 26 2006
STATUS
approved