A006081 Number of line-rooted projective plane trees with n nodes. (Formerly M2593)

1, 1, 3, 6, 17, 44, 133, 404, 1319, 4392, 15114, 52796, 187410, 671848, 2430509, 8852584, 32438603, 119463056, 441926206, 1641246060, 6117011262, 22871513128, 85766691938, 322479555096, 1215493792902, 4591852445104, 17383416640308, 65937045017304

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]

Index entries for sequences related to trees

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

Cf. A000108, A001405. - Alois P. Heinz, Feb 03 2009

Sequence in context: A216878 A237670 A321227 * A099511 A204517 A307685

Adjacent sequences: A006078 A006079 A006080 * A006082 A006083 A006084

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Feb 03 2009

Status

approved