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A107984
Triangle read by rows: T(n,k) = (k+1)*(n+2)*(2n-k+3)*(n-k+1)/6 for 0 <= k <= n.
2
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
OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids. Column 0 yields A000330. Main diagonal yields A000292. Row sums yield A006414.
LINKS
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 237, K{B(n,3,-l)}).
FORMULA
T(n-2,k-1) = n*(2*n-k)*(n-k)*k/6. - M. F. Hasler, Dec 26 2016
EXAMPLE
Triangle begins:
1;
5, 4;
14, 16, 10;
30, 40, 35, 20;
MAPLE
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
PROG
(PARI) A107984_row(n)=vector(n+1, k, k*(2*n-k+4)*(n-k+2))*(n+2)/6 \\ M. F. Hasler, Dec 26 2016
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved