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Search: id:A000226
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| A000226 |
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Number of n-node unlabeled connected graphs with one cycle of length 3.
(Formerly M2668 N1066)
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+0
6
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| 1, 1, 3, 7, 18, 44, 117, 299, 793, 2095, 5607, 15047, 40708, 110499, 301541, 825784, 2270211, 6260800, 17319689, 48042494, 133606943, 372430476, 1040426154, 2912415527, 8167992598, 22947778342, 64577555147
(list; graph; listen)
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OFFSET
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3,3
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COMMENT
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Number of rooted trees where root has degree 3. - Christian Bower (bowerc(AT)usa.net)
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 150.
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LINKS
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Index entries for sequences related to rooted trees
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FORMULA
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G.f.: (r(x)^3+3*r(x)*r(x^2)+2*r(x^3))/6 where r(x) is g. f. for rooted trees (A000081).
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MAPLE
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b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember; add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember; unapply (add (b(k)*x^k, k=1..n), x) end: a:= n-> coeff (series ((B(n-2)(x)^3+ 3*B(n-2)(x)* B(n-2)(x^2)+ 2*B(n-2)(x^3))/6, x=0, n+1), x, n): seq (a(n), n=3..29); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
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CROSSREFS
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Adjacent sequences: A000223 A000224 A000225 this_sequence A000227 A000228 A000229
Sequence in context: A129921 A036670 A027967 this_sequence A036883 A114713 A116413
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KEYWORD
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nonn,nice
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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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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 19 2000
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