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Search: id:A004113
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| A004113 |
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Number of rooted trees with n nodes and 2-colored non-leaf nodes.
(Formerly M1629)
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+0
5
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| 1, 2, 6, 18, 60, 204, 734, 2694, 10162, 38982, 151920, 599244, 2389028, 9608668, 38945230, 158904230, 652178206, 2690598570, 11151718166, 46412717826, 193891596436, 812748036380, 3417407089470
(list; graph; listen)
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OFFSET
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1,2
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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).
F. Harary, R. W. Robinson and A. J. Schwenk, Twenty-step algorithm for determining the asymptotic number of trees of various species, J. Austral. Math. Soc., Series A, 20 (1975), 483-503. Errata: Vol. A 41 (1986), p. 325.
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LINKS
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N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
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Shifts left and halves under EULER transform.
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MAPLE
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with (numtheory): etr:= proc(p) local b; b:= proc(n) option remember; if n=0 then 1 else (add (d*p(d), d=divisors(n)) +add (add(d*p(d), d=divisors(j)) *b(n-j), j=1..n-1))/n fi end end: b:= etr(a): a:= n-> if n<=1 then n else 2*b(n-1) fi: seq (a(n), n=1..23); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 06 2008]
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CROSSREFS
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Cf. A004114, A052316, A052317.
Sequence in context: A150043 A048117 A048118 this_sequence A150044 A108531 A150045
Adjacent sequences: A004110 A004111 A004112 this_sequence A004114 A004115 A004116
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KEYWORD
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nonn,eigen
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Extended with better description from Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.
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