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Search: id:A006414
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| A006414 |
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Number of nonseparable toroidal tree-rooted maps on n nodes.
(Formerly M4621)
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+0
7
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| 1, 9, 40, 125, 315, 686, 1344, 2430, 4125, 6655, 10296, 15379, 22295, 31500, 43520, 58956, 78489, 102885, 133000, 169785, 214291, 267674, 331200, 406250, 494325, 597051, 716184, 853615, 1011375, 1191640, 1396736, 1629144, 1891505, 2186625, 2517480, 2887221
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)= K(Oa(2,3,n)), Kekul\'e numbers of certain benzenoid structures (see the Cyvin - Gutman reference).
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REFERENCES
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Walsh, T. R. S.; Lehman, A. B.; Counting rooted maps by genus. III: Nonseparable maps. J. Combinatorial Theory Ser. B 18 (1975), 222-259.
S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988, p. 105, eq. (ii). 187).
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FORMULA
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a(n) = (n+1)*(n+2)^3*(n+3)/24. - njas, Apr 02 2004
a(n)=(n+2)^3((n+2)^2-1)/24 - Paul Richards (pr(AT)paulrichards.me.uk), Mar 04 2007
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MAPLE
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a:=n->sum(sum(sum((n-k)*k/4, j=1..n), k=1..n), m=1..n): seq(a(n), n=2..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 13 2007
with(combinat):a:=n->sum(sum(sum(binomial(n+2, 2)/12, j=1..n), k=0..n), m=0..n): seq(a(n), n=1..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 30 2007
a:=n->sum(n^4-n^3, j=0..n): seq(a(n)/24, n=2..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2008
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CROSSREFS
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Differences of A006542 (C(n, 3)*C(n-1, 3)/4).
Cf. A005891, A006322, A004068.
Cf. A133754.
Sequence in context: A076603 A003354 A063164 this_sequence A027137 A026629 A086349
Adjacent sequences: A006411 A006412 A006413 this_sequence A006415 A006416 A006417
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from Robert Newstedt (Patternfinder(AT)webtv.net).
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