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

%I A172397 #27 Dec 18 2022 06:38:33
%S A172397 1,1,2,2,3,3,4,4,4,3,1,-2,-7,-13,-22,-32,-45,-58,-72,-83,-90,-88,-73,
%T A172397 -39,21,113,245,420,642,905,1200,1502,1776,1965,1994,1763,1150,14,
%U A172397 -1799,-4437,-8026,-12629,-18212,-24578,-31311,-37691,-42625,-44568,-41476
%N A172397 a(n) = a(n-1) + a(n-2) - a(n-3) - a(n-8), starting 1,1,2,2,3,3,4,4.
%H A172397 G. C. Greubel, <a href="/A172397/b172397.txt">Table of n, a(n) for n = 0..1000</a>
%H A172397 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,0,0,0,-1).
%F A172397 G.f.: 1/(1 - x - x^2 + x^3 + x^8).
%t A172397 f[-6]=0; f[-5]=0; f[-4]=0; f[-3]=0; f[-2]=0; f[-1]=0; f[0]=1; f[1]=1;
%t A172397 f[n_]:= f[n] =f[n-1]+f[n-2]-f[n-3]-f[n-8]; Table[f[n], {n, 0, 50}]
%t A172397 LinearRecurrence[{1,1,-1,0,0,0,0,-1},{1,1,2,2,3,3,4,4},50] (* _Harvey P. Dale_, Nov 20 2012 *)
%o A172397 (PARI) my(x='x+O('x^50)); Vec(1/(1-x-x^2+x^3+x^8)) \\ _G. C. Greubel_, Mar 01 2019
%o A172397 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x-x^2+x^3+x^8) )); // _G. C. Greubel_, Mar 01 2019
%o A172397 (Sage) (1/(1-x-x^2+x^3+x^8)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Mar 01 2019
%o A172397 (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
%Y A172397 Cf. A023438.
%K A172397 sign,easy
%O A172397 0,3
%A A172397 _Roger L. Bagula_, Nov 20 2010
%E A172397 More terms from _Harvey P. Dale_, Nov 20 2012