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A051528
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Molien series for group G_{1,2} of order 384.
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1
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1, 0, 0, 0, 4, 2, 3, 2, 11, 7, 11, 9, 25, 18, 27, 23, 48, 38, 54, 47, 83, 69, 94, 84, 133, 114, 150, 136, 200, 176, 225, 206, 287, 257, 321, 297, 397, 360, 441, 411, 532, 488, 588, 551, 695, 643, 764, 720, 889, 828, 972, 920, 1116, 1046, 1215
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OFFSET
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0,5
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,1,-1,-1,1,-2,2,0,0,1,-1).
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FORMULA
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a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=4, a(5)=2, a(6)=3, a(7)=2, a(8)=11, a(9)=7, a(10)=11, a(11)=9, a(12)=25, a(13)=18, a(14)=27, a(n)=a(n-1)+ 2*a(n-4)- 2*a(n-5)+ a(n-6)- a(n-7)-a(n-8)+a(n-9)-2*a(n-10)+ 2*a(n-11)+ a(n-14)-a(n-15). - Harvey P. Dale, Mar 04 2013
G.f.: (x^12-x^9+2*x^8+2*x^4-x+1) / ((x-1)^4*(x+1)^3*(x^2-x+1)*(x^2+1)^2*(x^2+x+1)). - Colin Barker, Apr 02 2015
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MAPLE
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(1+x)*(1+x^2)*(1-x+2*x^4+2*x^8-x^9+x^12)/((1-x^4)^3*(1-x^6));
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1+x^2)*(1-x+2*x^4+2*x^8-x^9+x^12)/((1-x^4)^3*(1-x^6)), {x, 0, 60}], x] (* or *) LinearRecurrence[ {1, 0, 0, 2, -2, 1, -1, -1, 1, -2, 2, 0, 0, 1, -1}, {1, 0, 0, 0, 4, 2, 3, 2, 11, 7, 11, 9, 25, 18, 27}, 60] (* Harvey P. Dale, Mar 04 2013 *)
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PROG
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(PARI) Vec((x^12-x^9+2*x^8+2*x^4-x+1)/((x-1)^4*(x+1)^3*(x^2-x+1)*(x^2+1)^2*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Apr 02 2015
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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