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A047270
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Numbers that are congruent to {3, 5} mod 6.
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7
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3, 5, 9, 11, 15, 17, 21, 23, 27, 29, 33, 35, 39, 41, 45, 47, 51, 53, 57, 59, 63, 65, 69, 71, 75, 77, 81, 83, 87, 89, 93, 95, 99, 101, 105, 107, 111, 113, 117, 119, 123, 125, 129, 131, 135, 137, 141, 143, 147, 149
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OFFSET
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1,1
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COMMENTS
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Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 10 ).
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LINKS
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Link B. Berselli, Table of n, a(n) for n = 1..10000. [From Bruno Berselli, Jun 24 2010]
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))
William A. Stein, The modular forms database
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FORMULA
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a(n)=sqrt(2)sqrt((1-6n)(-1)^n+18n^2-6n+1)/2 - Paul Barry, May 11 2003
Contribution from Bruno Berselli, Jun 24 2010: (Start)
G.f.: (3+2*x+x^2)/((1+x)*(1-x)^2).
a(n)-a(n-1)-a(n-2)+a(n-3) = 0, with n>3.
a(n) = (6*n-(-1)^n-1)/2. (End)
a(n)=6*n-a(n-1)-4 (with a(1)=3) [From Vincenzo Librandi, Aug 05 2010]
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EXAMPLE
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For n=2, a(2)=6*2-3-4=5; n=3, a(3)=6*3-5-4=9; n=4, a(4)=6*4-9-4=11 [From Vincenzo Librandi, Aug 05 2010]
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CROSSREFS
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Cf. A047235 [(6*n-(-1)^n-3)/2], A047241 [(6*n-(-1)^n-5)/2], A047238 [(6*n-(-1)^n-7)/2]. [From Bruno Berselli, Jun 24 2010]
Subsequence of A186422.
Sequence in context: A109324 A190844 A191207 * A084060 A024896 A160771
Adjacent sequences: A047267 A047268 A047269 * A047271 A047272 A047273
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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