A108675 a(n) = (n+1)*(n+2)*(61*n^4 + 366*n^3 + 845*n^2 + 888*n + 360)/720.

1, 21, 157, 707, 2353, 6405, 15106, 31998, 62349, 113641, 196119, 323401, 513149, 787801, 1175364, 1710268, 2434281, 3397485, 4659313, 6289647, 8369977, 10994621, 14272006, 18326010, 23297365, 29345121, 36648171, 45406837

Offset: 0

Author

Emeric Deutsch, Jun 17 2005

Keywords

• nonn
• easy

Comments

Kekulé numbers for certain benzenoids.

References

• S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 231, # 35).

Links

• R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission] See p. 31.
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Programs

Maple

a:=n->(n+1)*(n+2)*(61*n^4+366*n^3+845*n^2+888*n+360)/720: seq(a(n),n=0..32);

Formula

G.f.: (1 + 14*x + 31*x^2 + 14*x^3 + x^4)/(1-x)^7.