OFFSET
2,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
P. K. Stockmeyer, The charm bracelet problem and its applications, pp. 339-349 of Graphs and Combinatorics (Washington, Jun 1973), Ed. by R. A. Bari and F. Harary. Lect. Notes Math., Vol. 406. Springer-Verlag, 1974.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..1000
P. J. Stockmeyer, The charm bracelet problem and its applications, pp. 339-349 of Graphs and Combinatorics (Washington, Jun 1973), Ed. by R. A. Bari and F. Harary. Lect. Notes Math., Vol. 406. Springer-Verlag, 1974. [Scanned annotated and corrected copy]
FORMULA
Stockmeyer gives g.f.
a(n) ~ 2^(2*n-4) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Sep 12 2014
MAPLE
b:= proc(n) option remember; binomial(n, floor(n/2)) end: c:= proc(n) option remember; binomial(2*n, n) /(n+1) end: a:= proc(m) local n; n:=m-2; (add(c(k)*c(n-k) +b(k)*b(n-k), k=0..n)) /4 +`if`(irem(n, 2)=0, c(n/2)/2, 0) end: seq(a(n), n=2..30); # Alois P. Heinz, Feb 03 2009
MATHEMATICA
b[n_] := Binomial[n, Floor[n/2]]; c[n_] := Binomial[2n, n]/(n+1); a[m_] := (n = m-2; Sum[c[k]*c[n-k] + b[k]*b[n-k], {k, 0, n}]/4 + If[Mod[n, 2] == 0, c[n/2]/2, 0]); Table[a[n], {n, 2, 30}] (* Jean-François Alcover, Jul 20 2011, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Alois P. Heinz, Feb 03 2009
STATUS
approved