A098574 a(n) = Sum_{k=0..floor(n/7)} C(n-5*k,2*k).

1, 1, 1, 1, 1, 1, 1, 2, 4, 7, 11, 16, 22, 29, 38, 51, 71, 102, 149, 218, 316, 452, 639, 897, 1257, 1766, 2493, 3536, 5031, 7165, 10196, 14484, 20538, 29085, 41168, 58282, 82561, 117036, 165995, 235492, 334074, 473824, 671856, 952449, 1350078, 1913702

Offset: 0

Author

Paul Barry, Sep 16 2004

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• R. Austin and R. K. Guy, Binary sequences without isolated ones, Fib. Quart., 16 (1978), 84-86.
• V. C. Harris, C. C. Styles, A generalization of Fibonacci numbers, Fib. Quart. 2 (1964) 277-289, sequence u(n,5,2).
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,1).

Crossrefs

Cf. A005251, A005252, A005253, A005689.

Programs

Magma

Q:=Rationals(); R:=PowerSeriesRing(Q, 40); Coefficients(R!((1-x)/(1-2*x+x^2-x^7))) // G. C. Greubel, Feb 03 2018

Mathematica

CoefficientList[Series[(1-x)/(1-2*x+x^2-x^7), {x,0,50}], x] (* G. C. Greubel, Feb 03 2018 *)

PARI

a(n) = sum(k=0, n\7, binomial(n-5*k, 2*k)); \\ Michel Marcus, Sep 06 2017

PARI

x='x+O('x^30); Vec((1-x)/(1-2*x+x^2-x^7)) \\ G. C. Greubel, Feb 03 2018

Formula

G.f.: (1-x)/(1-2*x+x^2-x^7).