A108667 Triangle read by rows: T(n,k) = 9k*n + 14(n+k) + 20 (0 <= k <= n).

20, 34, 57, 48, 80, 112, 62, 103, 144, 185, 76, 126, 176, 226, 276, 90, 149, 208, 267, 326, 385, 104, 172, 240, 308, 376, 444, 512, 118, 195, 272, 349, 426, 503, 580, 657, 132, 218, 304, 390, 476, 562, 648, 734, 820, 146, 241, 336, 431, 526, 621, 716, 811

Offset: 0

Author

Emeric Deutsch, Jun 14 2005

Keywords

• nonn
• tabl

Comments

Kekulé numbers for certain benzenoids. T(n,n) = 9n^2 + 28n + 20 = A051872(n+2).

Examples

			Triangle begins:
20;
34,57;
48,80,112;
62,103,144,185;
		

References

• S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 102).

Crossrefs

Cf. A051872.

Programs

Maple

T:=proc(n,k) if k<=n then 9*k*n+14*(n+k)+20 else 0 fi end: for n from 0 to 10 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form

Formula

G.f.: (20 - 6z - 3t*z + t^2*z^2 - 16t*z^2 - 4t^2*z^3)/((1-z)^2*(1-t*z)^3).