

A107980


Triangle read by rows: T(n,k)=(n+2)(k+1)(k+2)(k2n2)(k2n3)/24 for 0<=k<=n.


0



1, 5, 9, 14, 30, 40, 30, 70, 105, 125, 55, 135, 216, 280, 315, 91, 231, 385, 525, 630, 686, 140, 364, 624, 880, 1100, 1260, 1344, 204, 540, 945, 1365, 1755, 2079, 2310, 2430, 285, 765, 1360, 2000, 2625, 3185, 3640, 3960, 4125, 385, 1045, 1881, 2805, 3740
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OFFSET

0,2


COMMENTS

KekulĂ© numbers for certain benzenoids. Column 0 yields A000330. Main diagonal yields A006414. Row sums yield A006858.


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,3,l)}).


LINKS

Table of n, a(n) for n=0..49.


EXAMPLE

Triangle begins:
1;
5,9;
14,30,40;
30,70,105,125;


MAPLE

T:=proc(n, k) if k<=n then 1/24*(n+2)*(k+1)*(k+2)*(k2*n2)*(k2*n3) 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. A000330, A006414, A006858.
Sequence in context: A109329 A169872 A115380 * A163161 A331556 A188358
Adjacent sequences: A107977 A107978 A107979 * A107981 A107982 A107983


KEYWORD

nonn,tabl


AUTHOR

Emeric Deutsch, Jun 12 2005


STATUS

approved



