Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Feb 27 2015 09:27:03
%S 1,6,10,20,40,50,50,110,155,175,105,245,371,455,490,196,476,756,980,
%T 1120,1176,336,840,1380,1860,2220,2436,2520,540,1380,2325,3225,3975,
%U 4515,4830,4950,825,2145,3685,5225,6600,7700,8470,8910,9075,1210,3190
%N 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.
%C Kekulé numbers for certain benzenoids. Column 0 yields A002415. Main diagonal yields A006542.
%D 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)}).
%e Triangle begins:
%e 1;
%e 6,10;
%e 20,40,50;
%e 50,110,155,175;
%p 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
%Y Cf. A002415, A006542.
%K nonn,tabl
%O 0,2
%A _Emeric Deutsch_, Jun 12 2005