

A107972


Triangle read by rows: T(n,k) = (k+1)(k+2)(n+2)(3n2k+3)/12 for 0<=k<=n.


1



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
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OFFSET

0,2


COMMENTS

KekulĂ© 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, KekulĂ© 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*n2*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 A036252
Adjacent sequences: A107969 A107970 A107971 * A107973 A107974 A107975


KEYWORD

nonn,tabl


AUTHOR

Emeric Deutsch, Jun 12 2005


STATUS

approved



