

A007560


Number of planted identity trees where nonroot, nonleaf nodes an even distance from root are of degree 2.
(Formerly M0325)


3



1, 1, 1, 1, 2, 2, 4, 6, 10, 17, 29, 51, 89, 159, 284, 512, 930, 1692, 3101, 5698, 10515, 19464, 36143, 67296, 125622, 235050, 440756, 828142, 1558955, 2939761, 5552744, 10504222, 19899760, 37750091, 71704061, 136361602, 259618770, 494821629, 944074665
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OFFSET

1,5


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226228 (1995), 5772; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226228 (1995), 5772; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees


FORMULA

Shifts 2 places left under weigh transform.
a(n) ~ c * d^n / n^(3/2), d = 1.983229991815043367273184141..., c = 0.5857451140002020594085469... .  Vaclav Kotesovec, Aug 25 2014
G.f.: x + x^2 * Product_{n>=1} (1 + x^n)^a(n).  Ilya Gutkovskiy, May 09 2019


MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(a(i), j)*b(ni*j, i1), j=0..n/i)))
end:
a:= n> `if`(n<2, n, b(n2, n2)):
seq(a(n), n=1..50); # Alois P. Heinz, May 19 2013


MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j]*b[ni*j, i1], {j, 0, n/i}]]]; a[n_] := If[n<2, n, b[n2, n2]]; Table[a[n], {n, 1, 40}] (* JeanFrançois Alcover, Jan 27 2014, after Alois P. Heinz *)


CROSSREFS

Cf. A007562.
Column k=2 of A316074.
Sequence in context: A293673 A293505 A032307 * A032237 A276061 A216958
Adjacent sequences: A007557 A007558 A007559 * A007561 A007562 A007563


KEYWORD

nonn,nice,eigen


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Better description from Christian G. Bower, May 15 1998.


STATUS

approved



