OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Marcia Ascher, Mu torere: an analysis of a Maori game, Math. Mag. 60 (1987), no. 2, 90-100.
R. K. Guy & N. J. A. Sloane, Correspondence, 1985
A. Ivanyi, L. Lucz, T. Matuszka, and S. Pirzada, Parallel enumeration of degree sequences of simple graphs, Acta Univ. Sapientiae, Informatica, 4, 2 (2012) 260-288.
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]
N. J. A. Sloane, Classic Sequences
FORMULA
a(n) = (1/2) * (binomial(2*n-1, n) + binomial(n-1, floor(n/2))). - Michael Somos
a(n) = A034851(2*n-1, n-1).
Conjecture: n*(n-2)*a(n) - (5*n-3)*(n-2)*a(n-1) + 4*(n-2)*a(n-2) + 4*(5*n^2-27*n+37)*a(n-3) - 8*(2*n-7)*(n-4)*a(n-4) = 0. - R. J. Mathar, Nov 09 2013
MAPLE
A005654:=n->(1/2)*(binomial(2*n-1, n)+binomial(n-1, floor(n/2))): seq(A005654(n), n=1..40); # Wesley Ivan Hurt, Jan 29 2017
MATHEMATICA
Table[(Binomial[2n-1, n]+Binomial[n-1, Floor[n/2]])/2, {n, 30}] (* Harvey P. Dale, May 17 2012 *)
PROG
(PARI) C(n, k)=binomial(n, k)
a(n)=(1/2)*(C(2*n-1, n)+C(n-1, n\2))
(Magma) [((Binomial(2*n-1, n)+Binomial(n-1, Floor(n/2)))/2): n in [1..30]]; // Vincenzo Librandi, May 24 2012
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Sequence extended and description corrected by Christian G. Bower
STATUS
approved