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

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

Offset

0,3

Links

Table of n, a(n) for n=0..33.

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

Formula

a(n) = 2*a(n-1) -a(n-3) +a(n-4); 4 initial terms required.

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

Prog

(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

Crossrefs

Pairwise sums of A049856. Partial sums of A049864.

Sequence in context: A345234 A351360 A080889 * A092483 A351361 A324767

Adjacent sequences: A049855 A049856 A049857 * A049859 A049860 A049861

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved