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 A063196 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 7 ). 5
 0, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 23, 23, 25, 25, 27, 27, 29, 29, 31, 31, 33, 33, 35, 35, 37, 37, 39, 39, 41, 41, 43, 43, 45, 45, 47, 47, 49, 49, 51, 51, 53, 53, 55, 55, 57, 57, 59, 59, 61, 61, 63, 63, 65, 65, 67, 67, 69, 69, 71, 71, 73, 73, 75, 75, 77, 77, 79, 79, 81, 81, 83 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also, for n>1, number of involutions (i.e. elements of order 2) in the dihedral group D_(n-1). - Lekraj Beedassy, Oct 22 2004 Also, the chromatic number of the n-th triangular graph; i.e., the chromatic index (edge chromatic number) of the n-th complete graph. - Danny Rorabaugh, Nov 26 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 J. Sondow and E. W. Weisstein, MathWorld: Wallis Formula. William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N)). William A. Stein, The modular forms database. Eric Weisstein's World of Mathematics, Chromatic Number, Edge Chromatic Number, and Triangular Graph. Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA For n > 1, a(n-1) = (2n + 1 + (-1)^n)/2 (odd numbers appearing twice). - Lekraj Beedassy, Oct 22 2004 For n > 1, a(n) = 2*n - a(n-1), (with a(1)=1). - Vincenzo Librandi, Dec 06 2010 From Colin Barker, Sep 08 2013: (Start) a(n) = a(n-1) + a(n-2) - a(n-3) for n > 4. G.f.: -x^2*(x^2-2*x-1) / ((x-1)^2*(x+1)). (End) MATHEMATICA CoefficientList[Series[-x (x^2 - 2 x - 1) / ((x - 1)^2 (x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Nov 27 2018 *) LinearRecurrence[{1, 1, -1}, {0, 1, 3, 3}, 90] (* Harvey P. Dale, Sep 11 2024 *) PROG (PARI) concat([0], Vec(-x^2*(x^2-2*x-1)/((x-1)^2*(x+1)) + O(x^100))) \\ Colin Barker, Sep 08 2013 CROSSREFS Cf. A109613. Sequence in context: A127630 A267458 A109613 * A351744 A339110 A245150 Adjacent sequences: A063193 A063194 A063195 * A063197 A063198 A063199 KEYWORD nonn,easy,changed AUTHOR N. J. A. Sloane, Jul 10 2001 STATUS approved

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Last modified September 19 12:32 EDT 2024. Contains 376012 sequences. (Running on oeis4.)