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A063233
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Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 79 ).
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1
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6, 19, 33, 45, 59, 71, 85, 97, 111, 123, 137, 149, 163, 175, 189, 201, 215, 227, 241, 253, 267, 279, 293, 305, 319, 331, 345, 357, 371, 383, 397, 409, 423, 435, 449, 461, 475, 487, 501, 513, 527, 539, 553, 565, 579, 591, 605, 617, 631, 643
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OFFSET
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1,1
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LINKS
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FORMULA
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Except for the first term, a(n) = 26*(n-1) - a(n-1) (with a(2)=19). - Vincenzo Librandi, Dec 07 2010
a(n+2) = a(n) + 26 (n > 1);
a(2n+1) = a(2n) + 14 (n > 0);
a(2n) = a(2n-1) + 12 (n > 1);
a(n) = 13n - { 6 if n = 2k+1, k > 0; 7 otherwise }.
G.f.: x*(6 + 13*x + 8*x^2 - x^3)/(1 - x - x^2 + x^3). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/42 + tan(3*Pi/13)*Pi/26 . - Amiram Eldar, Jan 12 2024
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MATHEMATICA
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Join[{6}, Table[13*n - (13 + (-1)^n)/2, {n, 2, 50}]] (* Amiram Eldar, Jan 12 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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