A028289 Expansion of (1+x^2+x^3+x^5)/((1-x)(1-x^3)(1-x^4)(1-x^6)).

1, 1, 2, 4, 5, 7, 11, 13, 17, 23, 27, 33, 42, 48, 57, 69, 78, 90, 106, 118, 134, 154, 170, 190, 215, 235, 260, 290, 315, 345, 381, 411, 447, 489, 525, 567, 616, 658, 707, 763, 812, 868, 932, 988, 1052, 1124, 1188

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• C. Ahmed, P. Martin, and V. Mazorchuk, On the number of principal ideals in d-tonal partition monoids, arXiv preprint arXiv:1503.06718 [math.CO], 2015-2019.
• B. N. Cyvin et al., Enumeration of conjugated hydrocarbons: Hollow hexagons revisited, Structural Chem., 6 (1995), 85-88, equations (6) and (22).
• W. C. Huffman, The biweight enumerator of self-orthogonal binary codes, Discr. Math. Vol. 26 1979, pp. 129-143.
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,-2,-2,1,1,1,-1).

Programs

Maple

A117373 := proc(n) op(1+(n mod 6),[1,-2,-3,-1,2,3]) ; end proc:
A076118 := proc(n) coeftayl( x*(1-x)/(1-x+x^2)^2,x=0,n) ; end proc:
A028289 := proc(n) 1/108*n^3 +1/8*n^2 +55/108*n +29/48 +1/16*(-1)^n -2*(-1)^n*A117373(n+2)/27 +(-1)^n*A076118(n+1)/9; end proc:
seq(A028289(n),n=0..20) ; # R. J. Mathar, Mar 22 2011

Mathematica

CoefficientList[Series[(1+x^2+x^3+x^5)/((1-x)(1-x^3)(1-x^4) (1-x^6)),{x,0,50}],x]  (* Harvey P. Dale, Apr 20 2011 *)

PARI

Vec((1+x^2+x^3+x^5)/((1-x)*(1-x^3)*(1-x^4)*(1-x^6))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

G.f.: 1 / ( (1+x)*(1+x+x^2)^2*(x-1)^4 ). - R. J. Mathar, Mar 22 2011