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A006081
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Number of line-rooted projective plane trees with n nodes.
(Formerly M2593)
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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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.
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LINKS
| Index entries for sequences related to trees
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FORMULA
| Stockmeyer gives g.f.
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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); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Feb 03 2009]
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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}] (* From Jean-François Alcover, Jul 20 2011, after A. P. Heinz *)
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CROSSREFS
| Cf. A000108, A001405. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Feb 03 2009]
Sequence in context: A121399 A129905 A143363 * A099511 A204517 A143093
Adjacent sequences: A006078 A006079 A006080 * A006082 A006083 A006084
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Feb 03 2009
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