A099559 a(n) = Sum_{k=0..floor(n/5)} C(n-4k,k+1).

0, 1, 2, 3, 4, 5, 7, 10, 14, 19, 25, 33, 44, 59, 79, 105, 139, 184, 244, 324, 430, 570, 755, 1000, 1325, 1756, 2327, 3083, 4084, 5410, 7167, 9495, 12579, 16664, 22075, 29243, 38739, 51319, 67984, 90060, 119304, 158044, 209364, 277349, 367410, 486715

Offset: 0

Author

Paul Barry, Oct 22 2004

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Minerva Catral, P. L. Ford, P. E. Harris, S. J. Miller, et al. Legal Decompositions Arising from Non-positive Linear Recurrences, arXiv preprint arXiv:1606.09312 [math.CO], 2016. See Table 2.
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-1).

Crossrefs

Cf. A098578.

Programs

Mathematica

LinearRecurrence[{2,-1,0,0,1,-1},{0,1,2,3,4,5},50] (* Harvey P. Dale, Feb 20 2017 *)

PARI

a(n) = sum(k=0,n\5, binomial(n-4*k, k+1)); \\ Michel Marcus, Jul 11 2018

Formula

Partial sums of A003520 (with leading zero).

G.f.: x / ( (x-1)*(x^2-x+1)*(x^3+x^2-1) ).

a(n) = 2a(n-1)-a(n-2)+a(n-5)-a(n-6).

7*a(n) = A117373(n+2) -7 +10*b(n) +15*b(n-1) +9*b(n-2), where b(n) = A182097(n). - R. J. Mathar, Aug 07 2017

a(n) = A003520(n+4) -1. - R. J. Mathar, Aug 07 2017

Extensions

Values from a(5) on corrected by R. J. Mathar, Jul 29 2008