A001384 Number of n-node trees of height at most 4. (Formerly M1172 N0449)

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

0,4

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

Formula

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

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 *)

Crossrefs

See A001383 for details.

Sequence in context: A305380 A275862 A036622 * A089941 A307464 A127681

Adjacent sequences: A001381 A001382 A001383 * A001385 A001386 A001387

Keyword

nonn

Author

N. J. A. Sloane

Status

approved