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

1,1

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

Table of n, a(n) for n=1..20.

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

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

Maple

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

Crossrefs

Sequence in context: A337105 A056306 A056298 * A074574 A267899 A073514

Adjacent sequences: A114476 A114477 A114478 * A114480 A114481 A114482

Keyword

nonn,easy

Author

Emeric Deutsch, Nov 30 2005

Status

approved