A109537 a(0)=a(1)=a(2)=a(3)=a(4)=a(5)=1; a(n)=a(n-1)+a(n-2)-a(n-4)+a(n-6) for n>=6.

1, 1, 1, 1, 1, 1, 2, 3, 5, 8, 12, 18, 27, 40, 60, 90, 135, 203, 305, 458, 688, 1033, 1551, 2329, 3497, 5251, 7885, 11840, 17779, 26697, 40088, 60196, 90390, 135729, 203810, 306040, 459548, 690055, 1036183, 1555927, 2336372, 3508284, 5268021, 7910433

Offset: 0

Author

Roger L. Bagula, Jun 19 2005

Keywords

• nonn
• easy

Programs

Maple

a[0]:=1: a[1]:=1: a[2]:=1: a[3]:=1: a[4]:=1: a[5]:=1: for n from 6 to 45 do a[n]:=a[n-1]+a[n-2]-a[n-4]+a[n-6] od: seq(a[n],n=0..45);

Mathematica

F[1] = 1; F[2] = 1; F[3] = 1; F[4] = 1; F[5] = 1; F[6] = 1; F[n__] := F[n] = F[n - 1] + F[n - 2] - F[n - 4] + F[n - 6] aa = Table[F[n], {n, 1, 50}]

Formula

G.f.: (1-x^2-x^3)/(1-x-x^2+x^4-x^6).