A049863 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 0,3,4.

0, 3, 4, 7, 11, 21, 39, 74, 138, 258, 481, 898, 1676, 3129, 5841, 10904, 20355, 37998, 70933, 132415, 247187, 461439, 861396, 1608020, 3001788, 5603619, 10460614, 19527460, 36453089, 68049183, 127031520, 237137411, 442678728, 826375119, 1542644347, 2879747377

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

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

Programs

Mathematica

LinearRecurrence[{2,0,-1,1},{0,3,4,7},40] (* or *) CoefficientList[ Series[(x^3+2x^2-3x)/(x^4-x^3+2x-1),{x,0,50}],x] (* Harvey P. Dale, Apr 26 2011 *)

Formula

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

G.f.: (x^3+2x^2-3x)/(x^4-x^3+2x-1). - Harvey P. Dale, Apr 26 2011