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A108678 a(n) = (n+1)^2*(n+2)(2n+3)/6. 2

%I

%S 1,10,42,120,275,546,980,1632,2565,3850,5566,7800,10647,14210,18600,

%T 23936,30345,37962,46930,57400,69531,83490,99452,117600,138125,161226,

%U 187110,215992,248095,283650,322896,366080,413457,465290,521850,583416,650275,722722

%N a(n) = (n+1)^2*(n+2)(2n+3)/6.

%C Kekulé numbers for certain benzenoids.

%D S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 232, # 44).

%F G.f.: (1 + 5*x + 2*x^2)/(1-x)^5.

%F a(n) = A098077(n+1)/2. - _Alexander Adamchuk_, Apr 12 2006

%p a:=n->(n+1)^2*(n+2)*(2*n+3)/6: seq(a(n),n=0..42);

%p a:=n->sum(n*j^2, j=1..n): seq(a(n), n=1..36); # _Zerinvary Lajos_, Apr 29 2007

%t Table[(n+1)^2*(n+2)(2n+3)/6,{n,0,100}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 03 2011 *)

%Y Cf. A098077.

%K nonn,easy

%O 0,2

%A _Emeric Deutsch_, Jun 17 2005

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Last modified January 22 16:25 EST 2020. Contains 331152 sequences. (Running on oeis4.)