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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 10 2001
STATUS
approved