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A091426
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Expansion of (1 + x^18 + x^21 + x^22 + x^23 + x^24 + x^27 + x^45) / ( (1 - x^8)*(1 - x^12)*(1 - x^14)*(1 - x^15)).
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0
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1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 2, 2, 3, 0, 2, 2, 2, 2, 4, 2, 4, 2, 3, 4, 6, 4, 7, 5, 5, 4, 7, 5, 8, 8, 9, 8, 10, 7, 12, 11, 12, 12, 14, 10, 14, 13, 15, 16, 20, 16, 20, 18, 20, 20, 24, 21, 26, 24, 25, 25, 30, 26, 33, 32, 33, 33, 37, 33, 40, 38, 41, 42, 46, 41, 48
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OFFSET
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0,23
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COMMENTS
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Poincaré series [or Poincare series] (or Molien series) for F_2[x_1..x_4]^(A_7).
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REFERENCES
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A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004, last page of Chapter III.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1,0,0,0,0,0,0,1,-1,1,0,0,-1,1,0,-1,0,0,0,0,0,-1,0,1,-1,0,0,1,-1,1,0,0,0,0,0,0,1,-1,0,0,1,-1).
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MATHEMATICA
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CoefficientList[Series[(1+x^18+x^21+x^22+x^23+x^24+x^27+x^45)/((1-x^8)(1-x^12)(1-x^14)(1-x^15)), {x, 0, 100}], x] (* or *) LinearRecurrence[{1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, -1, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1}, {1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 2, 2, 3, 0, 2, 2, 2, 2, 4, 2, 4, 2, 3, 4, 6, 4, 7, 5, 5, 4, 7, 5, 8, 8}, 100] (* Harvey P. Dale, Oct 18 2023 *)
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PROG
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(PARI) Vec((1 + x^18 + x^21 + x^22 + x^23 + x^24 + x^27 + x^45) / ( (1 - x^8)*(1 - x^12)*(1 - x^14)*(1 - x^15)) + O(x^90)) \\ Michel Marcus, Jul 19 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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