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

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, 35, 36, 29, 35, 57, 71, 65, 64, 92, 128, 136, 129, 156, 220, 264, 265, 285, 376, 484, 529, 550, 661, 860, 1013, 1079, 1211, 1521, 1873, 2092, 2290, 2732, 3394, 3965

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Johann Cigler, Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials, arXiv:2212.02118 [math.NT], 2022.
• E. Wilson, The Scales of Mt. Meru
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1)

Programs

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

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

Mathematica

CoefficientList[Series[1/(1-x^4-x^5), {x, 0, 70}], x] (* Zerinvary Lajos, Mar 22 2007 *)

PARI

my(x='x+O('x^70)); Vec(1/(1-x^4-x^5)) \\ G. C. Greubel, Mar 05 2019

Sage

(1/(1-x^4-x^5)).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Mar 05 2019

Formula

G.f.: 1/(1-x^4-x^5).

a(n) = Sum_{k=0..floor(n/4)} binomial(k,n-4*k). - Seiichi Manyama, Mar 06 2019

Extensions

More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 17 1999