A117573 Expansion of (1+2x^2)/((1-x)(1-x^2)(1-x^3)).

1, 1, 4, 5, 8, 11, 15, 18, 24, 28, 34, 40, 47, 53, 62, 69, 78, 87, 97, 106, 118, 128, 140, 152, 165, 177, 192, 205, 220, 235, 251, 266, 284, 300, 318, 336, 355, 373, 394, 413, 434, 455, 477, 498, 522, 544, 568, 592, 617, 641, 668

Offset: 0

Author

Paul Barry, Mar 29 2006

Keywords

• easy
• nonn

Comments

Partial sums of A117572.

Links

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

Crossrefs

Cf. A117572.

Programs

Mathematica

CoefficientList[Series[(1+2x^2)/((1-x)(1-x^2)(1-x^3)),{x,0,50}],x] (* or *) LinearRecurrence[{1,1,0,-1,-1,1},{1,1,4,5,8,11},60] (* Harvey P. Dale, Jun 06 2013 *)

Formula

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

a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6).

a(n) = sqrt(3)*cos(2*Pi*n/3+Pi/6)/9 - sin(2*Pi*n/3+Pi/6)/3 + 3*cos(Pi*n)/8 + (6n^2+20n+15)/24.

a(n) = floor((9*(-1)^n + 6*n^2 + 20*n + 23)/24). - Tani Akinari, Nov 09 2012

a(n) = 1 - n/4 + n^2/4 + 3/2*floor(n/2) + floor((n+1)/3). - Vaclav Kotesovec, Jun 15 2014