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 A107981 Triangle read by rows: T(n,k) = (k+1)(k+2)(n+2)(n+3)(6n^2 - 8n*k + 18n + 3k^2 - 11k + 12)/144 for 0<=k<=n. 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS KekulĂ© numbers for certain benzenoids. Column 0 yields A002415. Main diagonal yields A006542. REFERENCES S. J. Cyvin and I. Gutman, KekulĂ© structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 237, K{F(n,3,l)}). LINKS EXAMPLE Triangle begins: 1; 6,10; 20,40,50; 50,110,155,175; MAPLE 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 CROSSREFS Cf. A002415, A006542. Sequence in context: A117348 A117349 A153369 * A065758 A254028 A085274 Adjacent sequences:  A107978 A107979 A107980 * A107982 A107983 A107984 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Jun 12 2005 STATUS approved

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Last modified June 14 05:51 EDT 2021. Contains 345018 sequences. (Running on oeis4.)