A113032 a(n) = Sum_{k=0..floor(n/8)} binomial(n-5*k, 3*k).

1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 21, 36, 57, 85, 121, 167, 228, 315, 449, 666, 1023, 1605, 2533, 3974, 6156, 9394, 14137, 21051, 31159, 46066, 68305, 101850, 152857, 230720, 349576, 530476, 804579, 1217951, 1838897, 2769267, 4161918, 6247570, 9375799

Offset: 0

Author

Alexey Kistanov (plast(AT)solid.ru), Jan 05 2006

Keywords

• nonn
• easy

Examples

			a(10+1)=11 because C(10,0) + C(5,3) = 1+10 = 11.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• R. Austin and R. K. Guy, Binary sequences without isolated ones, Fib. Quart., 16 (1978), 84-86.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,1).

Crossrefs

Cf. A005251, A005253, A000045.

Programs

Magma

[(&+[Binomial(n-5*k, 3*k): k in [0..Floor(n/8)]]): n in [0..50]]; // G. C. Greubel, Apr 09 2018

Mathematica

Table[Sum[Binomial[n - 5*k, 3*k], {k, 0, Floor[n/8]}], {n, 0, 50}] (* G. C. Greubel, Apr 09 2018 *)

PARI

a(n) = sum(k=0, n\8, binomial(n-5*k, 3*k)); \\ Michel Marcus, Sep 05 2013

PARI

lista(nn) = {my(x = xx + O(xx^nn)); gf = (1-x)^2/(1-3*x+3*x^2-x^3-x^8); for (i=0, nn-1, print1(polcoeff(gf, i, xx), ", "));} \\ Michel Marcus, Sep 05 2013

Sage

((1-x)^2/(1-3*x+3*x^2-x^3-x^8)).series(x, 44).coefficients(x, sparse=False) # Stefano Spezia, Aug 19 2023

Formula

G.f.: (1-x)^2/(1-3*x+3*x^2-x^3-x^8). [corrected by Georg Fischer, Apr 17 2020]

Extensions

Corrected by T. D. Noe, Nov 01 2006

More terms from Michel Marcus, Sep 05 2013