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Search: id:A007562
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| A007562 |
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Number of planted trees where non-root, non-leaf nodes an even distance from root are of degree 2.
(Formerly M0773)
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+0
3
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| 1, 1, 1, 2, 3, 6, 10, 20, 36, 72, 137, 275, 541, 1098, 2208, 4521, 9240, 19084, 39451, 82113, 171240, 358794, 753460, 1587740, 3353192, 7100909, 15067924, 32044456, 68272854, 145730675, 311575140, 667221030, 1430892924, 3072925944
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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There is no planted tree on one node by definition.
G.f. = x+x^2/(Product_{k>0}(1-x^k)^a(k)). - Michael Somos, Oct 06 2003
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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.
N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees
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FORMULA
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Shifts left 2 places 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 b(n-2) fi: seq (a(n), n=1..34); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 06 2008]
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PROGRAM
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(PARI) a(n)=local(A); if(n<2, n>0, A=x/(1-x)+O(x^n); for(k=2, n-2, A/=(1-x^k+O(x^n))^polcoeff(A, k-1)); polcoeff(A, n-1))
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CROSSREFS
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Sequence in context: A120421 A005418 A002215 this_sequence A008929 A066062 A164047
Adjacent sequences: A007559 A007560 A007561 this_sequence A007563 A007564 A007565
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KEYWORD
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nonn,nice,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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Better description from Christian G. Bower (bowerc(AT)usa.net), May 15 1998.
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