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G.f.: (1+x^2+3*x^3+4*x^4+4*x^5+4*x^6+3*x^7+x^8+x^10)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)).
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%I #8 Apr 14 2018 09:51:08

%S 1,0,2,4,7,10,16,22,31,40,54,66,85,102,126,150,179,208,246,282,327,

%T 370,424,476,539,600,672,744,827,908,1004,1096,1203,1308,1428,1546,

%U 1679,1810,1958,2104,2267,2426,2606,2782,2977,3170,3382,3592,3823,4050

%N G.f.: (1+x^2+3*x^3+4*x^4+4*x^5+4*x^6+3*x^7+x^8+x^10)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)).

%H H.-C. Herbig, D. Herden, C. Seaton, <a href="http://arxiv.org/abs/1404.1022">On compositions with x^2/(1-x)</a>, arXiv preprint arXiv:1404.1022, 2014. See Sect. 6.2.

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 1, 0, -1, -2, -1, 0, 1, 1, 1, 0, -1).

%t CoefficientList[Series[(1+x^2+3x^3+4x^4+4x^5+4x^6+3x^7+x^8+x^10)/ ((1- x^2) (1-x^3)(1-x^4)(1-x^5)),{x,0,50}],x] (* or *) LinearRecurrence[{0,1,1,1,0,-1,-2,-1,0,1,1,1,0,-1},{1,0,2,4,7,10,16,22,31,40,54,66,85,102},50] (* _Harvey P. Dale_, Apr 14 2018 *)

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Jul 04 2014