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A114239
a(n) = (n+1)(n+2)^3*(n+3)(n^2 + 4n + 5)/120.
3
1, 18, 136, 650, 2331, 6860, 17472, 39852, 83325, 162382, 298584, 522886, 878423, 1423800, 2236928, 3419448, 5101785, 7448874, 10666600, 15008994, 20786227, 28373444, 38220480, 50862500, 66931605, 87169446, 112440888, 143748766
OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
First differences of A107891. Partial sums of A083200. - Peter Bala, Sep 21 2007
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 167, Table 10.5/I/6).
LINKS
FORMULA
a(n-2) = (n^7-n^3)/(2^7-2^3). - David Radcliffe, Dec 27 2008
G.f.: (1+10*x+20*x^2+10*x^3+x^4)/(1-x)^8. - Colin Barker, Feb 09 2012
MAPLE
a:=n->(n+1)*(n+2)^3*(n+3)*(n^2+4*n+5)/120: seq(a(n), n=0..33);
PROG
(PARI) a(n)=n-=2; (n^7-n^3)/120 \\ Charles R Greathouse IV, Feb 09 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 18 2005
STATUS
approved