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A063210
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Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 42 ).
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2
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1, 2, 6, 6, 10, 10, 14, 14, 18, 18, 22, 22, 26, 26, 30, 30, 34, 34, 38, 38, 42, 42, 46, 46, 50, 50, 54, 54, 58, 58, 62, 62, 66, 66, 70, 70, 74, 74, 78, 78, 82, 82, 86, 86, 90, 90, 94, 94, 98, 98
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = (n^2 - n)/floor(n/2) for n >=2. (Excludes leading 1.) - William A. Tedeschi, Mar 20 2008
Except for the first term, a(n) = 4*(n-1) - a(n-1), (with a(2)=2). - Vincenzo Librandi, Dec 07 2010
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 4.
G.f.: -x*(x^3-3*x^2-x-1) / ((x-1)^2*(x+1)). (End)
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MATHEMATICA
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With[{c=Range[6, 102, 4]}, Join[{1, 2}, Riffle[c, c]]] (* or *) LinearRecurrence[ {1, 1, -1}, {1, 2, 6, 6, 10}, 50] (* Harvey P. Dale, Jun 22 2019 *)
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PROG
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(PARI) Vec(-x*(x^3-3*x^2-x-1)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Sep 08 2013
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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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