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 A047270 Numbers that are congruent to {3, 5} mod 6. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 10 ). LINKS 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 FORMULA 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] EXAMPLE 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] CROSSREFS 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 KEYWORD nonn AUTHOR STATUS approved

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