A107972 Triangle read by rows: T(n,k) = (k+1)(k+2)(n+2)(3n-2k+3)/12 for 0<=k<=n.

1, 3, 6, 6, 14, 20, 10, 25, 40, 50, 15, 39, 66, 90, 105, 21, 56, 98, 140, 175, 196, 28, 76, 136, 200, 260, 308, 336, 36, 99, 180, 270, 360, 441, 504, 540, 45, 125, 230, 350, 475, 595, 700, 780, 825, 55, 154, 286, 440, 605, 770, 924, 1056, 1155, 1210, 66, 186, 348

Offset

0,2

Comments

Kekulé numbers for certain benzenoids. Column 0 yields the triangular numbers (A000217). Row sums yield A006414. T(n,n) = A002415(n+2).

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{B(n,2,l)}).

Links

Table of n, a(n) for n=0..57.

Example

Triangle begins:
1;
3,6;
6,14,20;
10,25,40,50;

Maple

T:=proc(n, k) if k<=n then (k+1)*(k+2)*(n+2)*(3*n-2*k+3)/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

Crossrefs

Cf. A000217, A006414, A002415.

Sequence in context: A240250 A239424 A119306 * A238775 A269525 A341885

Adjacent sequences: A107969 A107970 A107971 * A107973 A107974 A107975

Keyword

nonn,tabl

Author

Emeric Deutsch, Jun 12 2005

Status

approved