A001895 Number of rooted planar 2-trees with n nodes.
1, 2, 4, 12, 34, 111, 360, 1226, 4206, 14728, 52024, 185824, 668676, 2424033, 8839632, 32412270, 119410390, 441819444, 1641032536, 6116579352, 22870649308, 85764947502, 322476066224, 1215486756372, 4591838372044
Offset: 1
References
- F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 78, (3.5.28).
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- T. D. Noe, Table of n, a(n) for n=1..200
- F. Harary and E. M. Palmer, Enumeration of self-converse digraphs, Mathematika, 13 (1966), 151-157.
- Index entries for sequences related to rooted trees
- Index entries for sequences related to trees
Programs
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Mathematica
Rest[CoefficientList[Series[(4-8x^2-Sqrt[1-4x]-(3+2x)Sqrt[1-4x^2])/ (8x^2),{x,0,30}],x]] (* Harvey P. Dale, Aug 08 2011 *)
Formula
G.f.: (4-8*x^2-sqrt(1-4*x)-(3+2*x)*sqrt(1-4*x^2))/(8*x^2).
a(n) ~ 4^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Aug 13 2013
Recurrence: (n+1)*(n+2)*(8*n^3 - 43*n^2 + 67*n - 36)*a(n) = 4*n*(n+1)*(8*n^3 - 39*n^2 + 41*n - 3)*a(n-1) + 4*(8*n^5 - 43*n^4 + 80*n^3 - 26*n^2 - 61*n + 36)*a(n-2) - 8*(n-3)*(2*n-3)*(8*n^3 - 19*n^2 + 5*n - 4)*a(n-3). - Vaclav Kotesovec, Aug 13 2013
Extensions
More terms from Vladeta Jovovic, Aug 24 2001