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

%I A028289 #29 Aug 09 2022 05:41:03
%S A028289 1,1,2,4,5,7,11,13,17,23,27,33,42,48,57,69,78,90,106,118,134,154,170,
%T A028289 190,215,235,260,290,315,345,381,411,447,489,525,567,616,658,707,763,
%U A028289 812,868,932,988,1052,1124,1188
%N A028289 Expansion of (1+x^2+x^3+x^5)/((1-x)(1-x^3)(1-x^4)(1-x^6)).
%H A028289 C. Ahmed, P. Martin, and V. Mazorchuk, <a href="http://arxiv.org/abs/1503.06718">On the number of principal ideals in d-tonal partition monoids</a>, arXiv preprint arXiv:1503.06718 [math.CO], 2015-2019.
%H A028289 B. N. Cyvin et al., <a href="http://dx.doi.org/10.1007/BF02281733">Enumeration of conjugated hydrocarbons: Hollow hexagons revisited</a>, Structural Chem., 6 (1995), 85-88, equations (6) and (22).
%H A028289 W. C. Huffman, <a href="http://dx.doi.org/10.1016/0012-365X(79)90119-5">The biweight enumerator of self-orthogonal binary codes</a>, Discr. Math. Vol. 26 1979, pp. 129-143.
%H A028289 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,-2,-2,1,1,1,-1).
%F A028289 G.f.: 1 / ( (1+x)*(1+x+x^2)^2*(x-1)^4 ). - _R. J. Mathar_, Mar 22 2011
%p A028289 A117373 := proc(n) op(1+(n mod 6),[1,-2,-3,-1,2,3]) ; end proc:
%p A028289 A076118 := proc(n) coeftayl( x*(1-x)/(1-x+x^2)^2,x=0,n) ; end proc:
%p A028289 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:
%p A028289 seq(A028289(n),n=0..20) ; # _R. J. Mathar_, Mar 22 2011
%t A028289 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 *)
%o A028289 (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
%K A028289 nonn,easy
%O A028289 0,3
%A A028289 _N. J. A. Sloane_