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Search: id:A107984
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| A107984 |
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Triangle read by rows: T(n,k)=(k+1)(n+2)(2n-k+3)(n-k+1)/6 for 0<=k<=n. |
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+0
1
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| 1, 5, 4, 14, 16, 10, 30, 40, 35, 20, 55, 80, 81, 64, 35, 91, 140, 154, 140, 105, 56, 140, 224, 260, 256, 220, 160, 84, 204, 336, 405, 420, 390, 324, 231, 120, 285, 480, 595, 640, 625, 560, 455, 320, 165, 385, 660, 836, 924, 935, 880, 770, 616, 429, 220, 506, 880
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Kekule numbers for certain benzenoids. Column 0 yields A000330. Main diagonal yields A000292. Row sums yield A006414.
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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 (p. 237, K{B(n,3,-l)}).
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EXAMPLE
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Triangle begins:
1;
5,4;
14,16,10;
30,40,35,20;
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MAPLE
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T:=proc(n, k) if k<=n then (k+1)*(n+2)*(2*n-k+3)*(n-k+1)/6 else 0 fi end: for n from 0 to 10 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000330, A000292, A006414.
Adjacent sequences: A107981 A107982 A107983 this_sequence A107985 A107986 A107987
Sequence in context: A019068 A078930 A094414 this_sequence A133178 A100791 A056883
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 12 2005
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