A000235 Number of n-node rooted trees of height 3.
0, 0, 0, 1, 3, 8, 18, 38, 76, 147, 277, 509, 924, 1648, 2912, 5088, 8823, 15170, 25935, 44042, 74427, 125112, 209411, 348960, 579326, 958077, 1579098, 2593903, 4247768, 6935070, 11290627, 18330973, 29684082, 47946852, 77258764, 124198083
Offset: 1
Keywords
References
- 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
- N. J. A. Sloane, Table of n, a(n) for n=1..200
- J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
- J. Riordan, The enumeration of trees by height and diameter, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)
- N. J. A. Sloane, Maple programs for counting rooted trees by height (after Riordan)
- Index entries for sequences related to rooted trees
- Index entries for sequences related to trees
Crossrefs
Column h=3 of A034781.
Programs
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Maple
# For Maple program see link. with(combstruct): ZL:= proc(m) local i; [T0, {seq(T||i=Prod(Z, Set(T||(i+1))), i=0..m-1), T||m=Z}, unlabeled] end: A000235:= n-> count(ZL(3), size=n)-count(ZL(2), size=n): seq(A000235(n), n=1..36); # Zerinvary Lajos, Sep 23 2007 -
Mathematica
m = 36; Rest @ CoefficientList[ Series[x*Product[(1-x^k)^(-PartitionsP[k-1]), {k, 1, m}], {x, 0, m}], x] - PartitionsP[Range[0, m-1]] (* Jean-François Alcover, Jul 05 2011, after Christian G. Bower *)
Comments