A140992 a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-2) + a(n-1) + A000071(n+1).

0, 1, 2, 5, 11, 23, 46, 89, 168, 311, 567, 1021, 1820, 3217, 5646, 9849, 17091, 29523, 50794, 87081, 148820, 253611, 431087, 731065, 1237176, 2089633, 3523226, 5930669, 9968123, 16730831, 28045222, 46954361, 78524160, 131181407

Offset: 0

Author

Juri-Stepan Gerasimov, Jul 08 2008

Keywords

• nonn
• easy

Examples

			If n = 4, then a(4) = a(4-2) + a(4-1) + A000071(4+1) = a(2) + a(3) + A000071(5) = 2 + 5 + 4 = 11.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,1,1).

Crossrefs

Cf. A000071, A000045, A140993, A140998.

Programs

Mathematica

LinearRecurrence[{3,-1,-3,1,1},{0,1,2,5,11},40] (* Harvey P. Dale, Jun 12 2014 *)

Formula

From R. J. Mathar, Apr 27 2010: (Start)

a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) + a(n-5).

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

a(n) = A140998(n+1, k = 2) = A140993(n+2, n) for n >= 1. - Petros Hadjicostas, Jun 10 2019

Extensions

Corrected (5980669 replaced by 5930669) by R. J. Mathar, Apr 27 2010