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%I #24 Oct 16 2021 15:40:30
%S 1,1,2,2,4,4,6,6,10,10,14,14,20,20,26,26,36,36,46,46,60,60,74,74,94,
%T 94,114,114,140,140,166,166,201,201,236,236,280,280,324,324,380,380,
%U 436,436,504,504,572,572,656,656,740,740,840,840,940,940,1060,1060,1180,1180,1320,1320,1460,1460,1625
%N Molien series of 5 X 5 upper triangular matrices over GF( 2 ).
%C Number of partitions of n into parts 1, 2, 4, 8, an 16. [_Joerg Arndt_, Jul 12 2013]
%D D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=243">Encyclopedia of Combinatorial Structures 243</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1).
%F G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)*(1-x^16)). [_Joerg Arndt_, Jul 12 2013]
%p 1/(1-x)/(1-x^2)/(1-x^4)/(1-x^8)/(1-x^16)
%t CoefficientList[Series[1/((1-x)(1-x^2)(1-x^4)(1-x^8)(1-x^16)),{x,0,70}],x] (* or *) LinearRecurrence[{1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,1},{1,1,2,2,4,4,6,6,10,10,14,14,20,20,26,26,36,36,46,46,60,60,74,74,94,94,114,114,140,140,166},70] (* _Harvey P. Dale_, Oct 16 2021 *)
%o (PARI) a(n)=floor((n^4+62*n^3+1271*n^2+9610*n+31125+(n+1)*(2*n^2+91*n+1179)*(-1)^n)/24576+1/512*(-1)^(n\2)*(n\2+1)*(n\2+15)+1/32*(-1)^(n\4)*(n\4+1)*(n%4>1)) \\ _Tani Akinari_, Jul 12 2013
%o (PARI) Vec(1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)*(1-x^16))+O(x^66)) \\ _Joerg Arndt_, Jul 12 2013
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_.
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