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Search: id:A107981
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| A107981 |
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Triangle read by rows: T(n,k)=(k+1)(k+2)(n+2)(n+3)(6n^2-8nk+18n+3k^2 -11k+12)/144 for 0<=k<=n. |
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+0
1
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| 1, 6, 10, 20, 40, 50, 50, 110, 155, 175, 105, 245, 371, 455, 490, 196, 476, 756, 980, 1120, 1176, 336, 840, 1380, 1860, 2220, 2436, 2520, 540, 1380, 2325, 3225, 3975, 4515, 4830, 4950, 825, 2145, 3685, 5225, 6600, 7700, 8470, 8910, 9075, 1210, 3190
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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 A002415. Main diagonal yields A006542.
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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{F(n,3,l)}).
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EXAMPLE
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Triangle begins:
1;
6,10;
20,40,50;
50,110,155,175;
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MAPLE
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T:=proc(n, k) if k<=n then 1/144*(k+1)*(k+2)*(n+2)*(n+3)*(6*n^2-8*n*k+18*n+3*k^2-11*k+12) else 0 fi end: for n from 0 to 9 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A002415, A006542.
Adjacent sequences: A107978 A107979 A107980 this_sequence A107982 A107983 A107984
Sequence in context: A095146 A117348 A117349 this_sequence A065758 A085274 A030007
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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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