A172397 a(n) = a(n-1) + a(n-2) - a(n-3) - a(n-8), starting 1,1,2,2,3,3,4,4.

1, 1, 2, 2, 3, 3, 4, 4, 4, 3, 1, -2, -7, -13, -22, -32, -45, -58, -72, -83, -90, -88, -73, -39, 21, 113, 245, 420, 642, 905, 1200, 1502, 1776, 1965, 1994, 1763, 1150, 14, -1799, -4437, -8026, -12629, -18212, -24578, -31311, -37691, -42625, -44568, -41476

Offset: 0

Author

Roger L. Bagula, Nov 20 2010

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,0,0,-1).

Crossrefs

Cf. A023438.

Programs

GAP

a:=[1,1,2,2,3,3,4,4];; for n in [9..50] do a[n]:=a[n-1]+a[n-2]-a[n-3]-a[n-8]; od; a; # G. C. Greubel, Mar 01 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x-x^2+x^3+x^8) )); // G. C. Greubel, Mar 01 2019

Mathematica

f[-6]=0; f[-5]=0; f[-4]=0; f[-3]=0; f[-2]=0; f[-1]=0; f[0]=1; f[1]=1;
f[n_]:= f[n] =f[n-1]+f[n-2]-f[n-3]-f[n-8]; Table[f[n], {n, 0, 50}]
LinearRecurrence[{1,1,-1,0,0,0,0,-1},{1,1,2,2,3,3,4,4},50] (* Harvey P. Dale, Nov 20 2012 *)

PARI

my(x='x+O('x^50)); Vec(1/(1-x-x^2+x^3+x^8)) \\ G. C. Greubel, Mar 01 2019

Sage

(1/(1-x-x^2+x^3+x^8)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Mar 01 2019

Formula

G.f.: 1/(1 - x - x^2 + x^3 + x^8).

Extensions

More terms from Harvey P. Dale, Nov 20 2012