A001384 Number of n-node trees of height at most 4.

1, 1, 1, 2, 4, 9, 19, 42, 89, 191, 402, 847, 1763, 3667, 7564, 15564, 31851, 64987, 132031, 267471, 539949, 1087004, 2181796, 4367927, 8721533, 17372967, 34524291, 68456755, 135446896, 267444085, 527027186, 1036591718, 2035083599

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n+1) is also the number of n-vertex graphs that do not contain a P_4, C_4, or K_5 as induced subgraph (K_5-free trivially perfect graphs, cf. A123467). - Falk Hüffner, Jan 10 2016

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=0..200
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 63
• J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
• N. J. A. Sloane, Transforms
• Index entries for sequences related to rooted trees
• Index entries for sequences related to trees

Crossrefs

See A001383 for details.

Programs

Maple

For Maple program see link in A000235.
with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d,j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: A000041:= etr(n->1): b1:= etr(k-> A000041(k-1)): A001383:= n->`if`(n=0,1,b1(n-1)): b2:= etr(A001383): a:= n->`if`(n=0,1,b2(n-1)): seq(a(n), n=0..40); # Alois P. Heinz, Sep 08 2008

Mathematica

Prepend[Nest[CoefficientList[Series[Product[1/(1-x^i)^#[[i]],{i,1,Length[#]}],{x,0,40}],x]&,{1},4],1] (* Geoffrey Critzer, Aug 01 2013 *)

Formula

Take Euler transform of A001383 and shift right. (Christian G. Bower)