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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)
16
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
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
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(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-François Alcover, Jan 27 2014, after Alois P. Heinz *)
CROSSREFS
Cf. A007562.
Column k=2 of A316074.
Sequence in context: A344707 A293505 A032307 * A032237 A276061 A216958
KEYWORD
nonn,nice,eigen
AUTHOR
EXTENSIONS
Better description from Christian G. Bower, May 15 1998
STATUS
approved

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Last modified February 25 02:17 EST 2024. Contains 370308 sequences. (Running on oeis4.)