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A007560 Number of planted identity trees where non-root, non-leaf 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 (list; graph; refs; listen; history; text; internal format)
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, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; 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

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

a:= n-> `if`(n<2, n, b(n-2, n-2)):

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[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := If[n<2, n, b[n-2, n-2]]; Table[a[n], {n, 1, 40}] (* Jean-Fran├žois 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

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Last modified October 20 07:17 EDT 2018. Contains 316378 sequences. (Running on oeis4.)