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A017827 a(n) = a(n-4) + a(n-5), with a(0)=1, a(1)=a(2)=a(3)=0, a(4)=1.

%I A017827 #31 Dec 19 2022 17:31:31
%S A017827 1,0,0,0,1,1,0,0,1,2,1,0,1,3,3,1,1,4,6,4,2,5,10,10,6,7,15,20,16,13,22,
%T A017827 35,36,29,35,57,71,65,64,92,128,136,129,156,220,264,265,285,376,484,
%U A017827 529,550,661,860,1013,1079,1211,1521,1873,2092,2290,2732,3394,3965
%N A017827 a(n) = a(n-4) + a(n-5), with a(0)=1, a(1)=a(2)=a(3)=0, a(4)=1.
%H A017827 Seiichi Manyama, <a href="/A017827/b017827.txt">Table of n, a(n) for n = 0..10000</a>
%H A017827 Johann Cigler, <a href="https://arxiv.org/abs/2212.02118">Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials</a>, arXiv:2212.02118 [math.NT], 2022.
%H A017827 E. Wilson, <a href="http://www.anaphoria.com/meruone.PDF">The Scales of Mt. Meru</a>
%H A017827 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,1)
%F A017827 G.f.: 1/(1-x^4-x^5).
%F A017827 a(n) = Sum_{k=0..floor(n/4)} binomial(k,n-4*k). - _Seiichi Manyama_, Mar 06 2019
%t A017827 CoefficientList[Series[1/(1-x^4-x^5), {x, 0, 70}], x] (* _Zerinvary Lajos_, Mar 22 2007 *)
%o A017827 (PARI) my(x='x+O('x^70)); Vec(1/(1-x^4-x^5)) \\ _G. C. Greubel_, Mar 05 2019
%o A017827 (Magma) I:=[1,0,0,0,1]; [n le 5 select I[n] else Self(n-4) +Self(n-5): n in [1..70]]; // _G. C. Greubel_, Mar 05 2019
%o A017827 (Sage) (1/(1-x^4-x^5)).series(x, 70).coefficients(x, sparse=False) # _G. C. Greubel_, Mar 05 2019
%o A017827 (GAP) a:=[1,0,0,0,1];; for n in [6..70] do a[n]:=a[n-4]+a[n-5]; od; a; # _G. C. Greubel_, Mar 05 2019
%K A017827 nonn,easy
%O A017827 0,10
%A A017827 _N. J. A. Sloane_
%E A017827 More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 17 1999