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.

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

Offset: 0

Author

Emeric Deutsch, Jun 12 2005

Keywords

• nonn
• tabl

Comments

Kekulé numbers for certain benzenoids. Column 0 yields A002415. Main diagonal yields A006542.

Examples

			Triangle begins:
1;
6,10;
20,40,50;
50,110,155,175;
		

References

• S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 237, K{F(n,3,l)}).

Crossrefs

Cf. A002415, A006542.

Programs

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