A049858 a(n) = Sum{a(k): k=0,1,2,...,n-4,n-2,n-1}; a(n-3) is not a summand; initial terms are 0,1,2.

0, 1, 2, 3, 5, 9, 17, 32, 60, 112, 209, 390, 728, 1359, 2537, 4736, 8841, 16504, 30809, 57513, 107363, 200421, 374138, 698426, 1303794, 2433871, 4543454, 8481540, 15833003, 29556423, 55174760, 102998057, 192272694, 358927051, 670030805, 1250786973, 2334919589

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,0,-1,1).

Crossrefs

Pairwise sums of A049856. Partial sums of A049864.

Programs

PARI

a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; 1,-1,0,2]^n*[0;1;2;3])[1,1] \\ Charles R Greathouse IV, Aug 16 2017

Formula

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

G.f. x*(x-1)*(1+x) / ( -1+2*x-x^3+x^4 ). - R. J. Mathar, Nov 12 2012

a(n) = A059633(n+2)-A059633(n). - R. J. Mathar, Aug 16 2017