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%I #10 Jun 13 2015 00:51:17
%S 1,1,3,5,10,15,26,37,57,79,112,149,202,260,338,425,536,659,812,980,
%T 1184,1408,1673,1963,2302,2670,3094,3554,4077,4642,5279,5964,6730,
%U 7552,8463,9438,10513,11659,12915,14252,15709,17256,18935,20713,22635,24667,26854
%N G.f.: (1+x^3+x^4+x^5+x^6+x^9)/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^4)).
%C Molien series for permutation representation of S_4 on pairs of elements from a set of size 4.
%D H. Derksen and G. Kemper, Computational Invariant Theory, Springer, 2002; p. 92.
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,0,-2,2,0,1,0,-2,1).
%F G.f.: ( -1+x-x^2-x^6+x^7-x^8-x^4 ) / ( (1+x+x^2)*(x^2+1)*(1+x)^2*(x-1)^5 ). - _R. J. Mathar_, Dec 18 2014
%F a(n)=2*a(n-1)-a(n-3)-2*a(n-5)+2*a(n-6)+a(n-8)-2*a(n-10)+a(n-11) for n>10. - _Harvey P. Dale_, Apr 10 2015
%t CoefficientList[Series[(1+x^3+x^4+x^5+x^6+x^9)/((1-x)(1-x^2)^2(1-x^3)(1-x^4)),{x,0,50}],x] (* or *) LinearRecurrence[{2,0,-1,0,-2,2,0,1,0,-2,1},{1,1,3,5,10,15,26,37,57,79,112},50] (* _Harvey P. Dale_, Apr 10 2015 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Feb 02 2004
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