A114239 a(n) = (n+1)(n+2)^3*(n+3)(n^2 + 4n + 5)/120.

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

Author

Emeric Deutsch, Nov 18 2005

Keywords

• nonn
• easy

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

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A047819, A083200, A107891.

Programs

Maple

a:=n->(n+1)*(n+2)^3*(n+3)*(n^2+4*n+5)/120: seq(a(n),n=0..33);

PARI

a(n)=n-=2;(n^7-n^3)/120 \\ Charles R Greathouse IV, Feb 09 2012

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