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A007560
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Number of planted identity trees where non-root, non-leaf nodes an even distance from root are of degree 2.
(Formerly M0325)
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16
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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
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1,5
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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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]
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FORMULA
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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
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MAPLE
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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)):
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,nice,eigen
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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