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Search: id:A123349
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| A123349 |
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Square array of Kekule numbers for the mirror-symmetrical chevrons Ch(m,n), read by antidiagonals (m,n>=0). |
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+0
1
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| 1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 14, 10, 1, 1, 5, 30, 46, 17, 1, 1, 6, 55, 146, 117, 26, 1, 1, 7, 91, 371, 517, 251, 37, 1, 1, 8, 140, 812, 1742, 1476, 478, 50, 1, 1, 9, 204, 1596, 4878, 6376, 3614, 834, 65, 1, 1, 10, 285, 2892, 11934, 22252, 19490, 7890, 1361, 82, 1, 1, 11
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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T(m,1)=A002522(m); T(m,2)=A123350(m); T(m,3)=A123351(m).
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REFERENCES
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S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see pp. 119-120).
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FORMULA
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T(m,n)=Sum((binom(m+i-1,i))^2, i=0..n).
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EXAMPLE
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T(1,1)=2 because Ch(1,1) consists of a single hexagon; it has 2 perfect matchings: {1,3,5} and {2,4,6}, the edges of the hexagon being labeled consecutively by 1,2,3,4,5,6.
Square array starts:
1 1 1 1 1 1 1 1...
1 2 3 4 5 6 7 8...
1 5 14 30 55 91 140 204 ...
1 10 46 146 371 812 1596 2892 ...
1 17 117 517 1742 4878 11934 26334 ...
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MAPLE
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T:=(m, n)->sum(binomial(m+i-1, i)^2, i=0..n): TT:=(m, n)->T(m-1, n-1): matrix(9, 9, TT); # yields sequence in matrix form
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CROSSREFS
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Cf. A002522, A123350, A123351.
Sequence in context: A112338 A111672 A128198 this_sequence A123352 A114163 A090234
Adjacent sequences: A123346 A123347 A123348 this_sequence A123350 A123351 A123352
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 14 2006
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EXTENSIONS
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Edited by Emeric Deutsch, Oct 27 2006, Oct 28 2006
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