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A051274
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Expansion of (1+x^4)/((1-x^2)*(1-x^3)).
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5
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1, 0, 1, 1, 2, 1, 3, 2, 3, 3, 4, 3, 5, 4, 5, 5, 6, 5, 7, 6, 7, 7, 8, 7, 9, 8, 9, 9, 10, 9, 11, 10, 11, 11, 12, 11, 13, 12, 13, 13, 14, 13, 15, 14, 15, 15, 16, 15, 17, 16, 17, 17, 18, 17, 19, 18, 19, 19, 20, 19, 21, 20, 21, 21, 22, 21, 23, 22, 23, 23, 24, 23, 25
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OFFSET
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0,5
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COMMENTS
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Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 3 ).
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LINKS
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FORMULA
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a(n) = 2*floor(n/2) + floor(n/3) - n + 1. Also a(0) = 1 and a(1) = 0, a(n) = a(n-2) + (a(n-1) reduced = (mod 2)). Again, a(0) = 1, a(1) = 0, a(n) = a(n-1) - 1 - (-1)^n - (a(n-2) mod 2). - Benoit Cloitre and Philippe Deléham, Jan 17 2004
Euler transform of length 8 sequence [ 0, 1, 1, 1, 0, 0, 0, -1]. - Michael Somos, Sep 26 2006
G.f.: (1-x^8)/((1-x^2)*(1-x^3)*(1-x^4)). a(n) = a(n-6) + 2. a(-1-n) = -a(n). - Michael Somos, Sep 26 2006
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MATHEMATICA
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CoefficientList[Series[(1-x^8)/((1-x^2)*(1-x^3)*(1-x^4)), {x, 0, 90}], x] (* or *) LinearRecurrence[{0, 1, 1, 0, -1}, {1, 0, 1, 1, 2}, 90] (* Harvey P. Dale, Feb 20 2013 *)
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PROG
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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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