A190912 Partial sums of pentanacci numbers (A000322).

1, 2, 3, 4, 5, 10, 19, 36, 69, 134, 263, 516, 1013, 1990, 3911, 7688, 15113, 29710, 58407, 114824, 225737, 443786, 872459, 1715208, 3372009, 6629194, 13032651, 25621516, 50370573, 99025938, 194679867, 382730540, 752428429, 1479235342, 2908100111, 5717174284

Offset: 1

Author

Harvey P. Dale, May 23 2011

Keywords

• nonn
• easy
• changed

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..3402
• Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,0,-1).

Crossrefs

Cf. A000322.

Programs

Mathematica

Accumulate[LinearRecurrence[{1,1,1,1,1},{1,1,1,1,1},50]] (* or *) LinearRecurrence[{2,0,0,0,0,-1},{1,2,3,4,5,10},50] (* Harvey P. Dale, May 23 2011 *)

Formula

a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=10, a(n) = 2*a(n-1)-a(n-6). - Harvey P. Dale, May 23 2011

G.f.: x*( 1-x^2-2*x^3-3*x^4 ) / ( (x-1)*(x^5+x^4+x^3+x^2+x-1) ). - R. J. Mathar, May 26 2011