A107332 Expansion of x^2*(-1+x+x^2)/(-1+x+x^2-x^3+x^5).

0, 1, 0, 0, -1, -1, -1, -1, -1, -2, -3, -5, -7, -10, -14, -20, -29, -42, -61, -88, -127, -183, -264, -381, -550, -794, -1146, -1654, -2387, -3445, -4972, -7176, -10357, -14948, -21574, -31137, -44939, -64859, -93609, -135103, -194990, -281423, -406169, -586211, -846060, -1221092, -1762364

Offset: 1

Author

Roger L. Bagula, Jun 08 2005

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,1).

Programs

Maple

a[0]:=0:a[1]:=1:a[2]:=0:a[3]:=0:a[4]:=-1:
for n from 5 to 46 do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-5] od:
seq(a[n],n=0..46);

Mathematica

LinearRecurrence[{1,1,-1,0,1},{0,1,0,0,-1},50] (* Harvey P. Dale, Oct 11 2015 *)

Formula

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-5) for n>=5.

O.g.f.: x^2*(-1+x+x^2)/(-1+x+x^2-x^3+x^5). - R. J. Mathar, Dec 02 2007

a(n) = A107293(n+2)-A107293(n+1)-A107293(n). - R. J. Mathar, Dec 17 2017

Extensions

Edited by N. J. A. Sloane, May 13 2006

New name using g.f. from Joerg Arndt, Dec 26 2022