%I A108674
%S A108674 1,15,84,300,825,1911,3920,7344,12825,21175,33396,50700,74529,106575,
%T A108674 148800,203456,273105,360639,469300,602700,764841,960135,1193424,
%U A108674 1470000,1795625,2176551,2619540,3131884,3721425,4396575,5166336
%N A108674 (n+1)^2*(n+2)^2*(2*n+3)/12.
%C A108674 Kekule numbers for certain benzenoids.
%C A108674 This is the case P(3,n) of the family of sequences defined in A132458. 
               - Ottavio D'Antona (dantona(AT)dico.unimi.it), Oct 31 2007
%D A108674 S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, 
               Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p.231, 
               # 33).
%F A108674 G.f.=(1+z)(1+8z+z^2)/(1-z)^6
%F A108674 Also a(n) = Sum[Sum[i*j^2, {i, 1, n+1}], {j, 1, n+1}]. - Alexander Adamchuk 
               (alex(AT)kolmogorov.com), Jun 25 2006
%p A108674 a:=n->(n+1)^2*(n+2)^2*(2*n+3)/12: seq(a(n),n=0..35);
%p A108674 a:=n->sum(k^2*sum(k, k=0..n), k=0..n):seq(a(n), n=1...31); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Aug 01 2008
%p A108674 a:=n->sum(k^2*sum(k, k=0..n), k=0..n):seq(a(n), n=1...31); [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Aug 09 2008]
%Y A108674 Sequence in context: A102360 A060581 A065103 this_sequence A050405 A020136 
               A067401
%Y A108674 Adjacent sequences: A108671 A108672 A108673 this_sequence A108675 A108676 
               A108677
%K A108674 nonn
%O A108674 0,2
%A A108674 Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 17 2005