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Search: id:A107983
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| A107983 |
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Triangle read by rows: T(n,k)=(k+1)(n+2)(n+3)(n-k+2)(n-k+1)/12 for 0<=k<=n. |
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+0
1
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| 1, 6, 4, 20, 20, 10, 50, 60, 45, 20, 105, 140, 126, 84, 35, 196, 280, 280, 224, 140, 56, 336, 504, 540, 480, 360, 216, 84, 540, 840, 945, 900, 750, 540, 315, 120, 825, 1320, 1540, 1540, 1375, 1100, 770, 440, 165, 1210, 1980, 2376, 2464, 2310, 1980, 1540
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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 A000292. Row sums yield A006542.
T(n,k) = number of Dyck (n+4)-paths with 4 peaks (UDs) and last descent of length k+1. For example, T(1,1)=4 counts UUDUDUDUDD, UDUUDUDUDD, UDUDUUDUDD, UDUDUDUUDD. - David Callan (callan(AT)stat.wisc.edu), Jun 26 2006
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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;
6,4;
20,20,10;
50,60,45,20;
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MAPLE
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T:=proc(n, k) if k<=n then (k+1)*(n+2)*(n+3)*(n-k+2)*(n-k+1)/12 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. A002415, A000292, A006542.
Adjacent sequences: A107980 A107981 A107982 this_sequence A107984 A107985 A107986
Sequence in context: A131828 A096038 A083581 this_sequence A009278 A120462 A061592
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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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