A114479 Kekulé numbers for certain benzenoids.

3, 20, 136, 928, 6336, 43264, 295424, 2017280, 13774848, 94060544, 642285568, 4385800192, 29948116992, 204498534400, 1396403339264, 9535238438912, 65110680797184, 444603538866176, 3035942864551936, 20730714605486080

Offset: 1

Author

Emeric Deutsch, Nov 30 2005

Keywords

• nonn
• easy

References

• S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 205).

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-8).

Programs

Maple

a:=((4+sqrt(8))^(n+1)+(4-sqrt(8))^(n+1))/16: seq(expand(a(n)),n=1..23);

Formula

a(n) = ((4+sqrt(8))^(n+1) + (4-sqrt(8))^(n+1))/16.

a(n) = 8*a(n-1) - 8*a(n-2). - Colin Barker, Aug 30 2013

G.f.: -x*(4*x-3) / (8*x^2 - 8*x + 1). - Colin Barker, Aug 30 2013

a(n)= 3*A057084(n-1) - 4*A057084(n-2). - R. J. Mathar, Aug 30 2013

a(n) = A007052(n+1)*2^(n-1). - R. J. Mathar, Jul 24 2022