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A097535
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Dimensions of spaces of cusp forms.
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0
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1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9, 9, 9, 12, 12, 12, 13, 13, 13, 14, 14, 15, 16, 16, 16, 17, 17, 17, 18, 19, 19, 20, 20, 20, 21, 21, 21, 24, 24, 24, 25, 25, 25, 26, 26, 27, 28, 28, 28, 29, 29, 29, 30, 31, 31, 32, 32, 32, 33, 33, 33, 36, 36, 36, 37, 37, 37, 38, 38, 39, 40, 40, 40, 41, 41, 41, 42, 43, 43, 44, 44, 44, 45, 45, 45, 48, 48, 48, 49
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OFFSET
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4,4
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REFERENCES
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H. Petersson, Modulfunktionen und Quadratische Formen, Springer-Verlag, 1982; p. 186.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
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FORMULA
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a(n+24m) = a(n) + 12m for m >= 1.
a(n)= +a(n-1) +a(n-24) -a(n-25). - R. J. Mathar, Oct 01 2011
G.f.: x^4*(1 + x^3 + x^5 + x^6 + x^9 + x^12 + x^13 + x^15 + x^18 + 3*x^21) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)*(1 + x^4)*(1 - x^4 + x^8)). - Colin Barker, Jun 06 2019
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9, 9, 9, 12, 12, 12, 13}, 120] (* Harvey P. Dale, May 11 2016 *)
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PROG
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(PARI) Vec(x^4*(1 + x^3 + x^5 + x^6 + x^9 + x^12 + x^13 + x^15 + x^18 + 3*x^21) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)*(1 + x^4)*(1 - x^4 + x^8)) + O(x^40)) \\ Colin Barker, Jun 06 2019
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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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