login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
J. Sondow and E. W. Weisstein, MathWorld: Wallis Formula.
William A. Stein, The modular forms database.
Eric Weisstein's World of Mathematics, Chromatic Number, Edge Chromatic Number, and Triangular Graph.
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 *)
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 10 2001
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)