A114480 Kekulé numbers for certain benzenoids.

4, 50, 650, 8500, 111250, 1456250, 19062500, 249531250, 3266406250, 42757812500, 559707031250, 7326660156250, 95907226562500, 1255441894531250, 16433947753906250, 215123168945312500, 2815998840332031250

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..17.

Index entries for linear recurrences with constant coefficients, signature (15,-25).

Formula

a(n) = 2*((sqrt(5) + 2)((15 + 5*sqrt(5))/2)^(n-1) + (sqrt(5) - 2)*((15 - 5*sqrt(5))/2)^(n-1))/sqrt(5).

From Colin Barker, Aug 30 2013: (Start)

a(n) = 15*a(n-1) - 25*a(n-2).

G.f.: -2*x*(5*x-2) / (25*x^2 - 15*x + 1). (End)

Maple

a:=2*((sqrt(5)+2)*((15+5*sqrt(5))/2)^(n-1)+(sqrt(5)-2)*((15-5*sqrt(5))/2)^(n-1))/sqrt(5): seq(expand(a(n)), n=1..20);

Mathematica

LinearRecurrence[{15, -25}, {4, 50}, 20] (* Harvey P. Dale, Oct 01 2023 *)

Crossrefs

Sequence in context: A232731 A215792 A280358 * A123356 A234870 A139087

Adjacent sequences: A114477 A114478 A114479 * A114481 A114482 A114483

Keyword

nonn

Author

Emeric Deutsch, Nov 30 2005

Status

approved