A123358 Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).

1, 10, 125, 1625, 21250, 278125, 3640625, 47656250, 623828125, 8166015625, 106894531250, 1399267578125, 18316650390625, 239768066406250, 3138604736328125, 41084869384765625, 537807922363281250, 7039997100830078125, 92154758453369140625, 1206321449279785156250, 15790952777862548828125, 206706255435943603515625

Offset

0,2

Links

Table of n, a(n) for n=0..21.

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 210, formula page 204).

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

Formula

G.f.: -(5*x-1) / (25*x^2-15*x+1). - Colin Barker, Aug 29 2013

a(n) = 5^n*A001519(n+1). - R. J. Mathar, Jul 26 2019

Maple

A123358 := proc(n)
    option remember;
    if n <= 1 then
        op(n+1, [1, 10]) ;
    else
        15*procname(n-1)-25*procname(n-2) ;
    end if
end proc:
seq( A123358(n), n=0..30) ; # R. J. Mathar, Jul 26 2019

Mathematica

LinearRecurrence[{15, -25}, {1, 10}, 30] (* Jean-François Alcover, Apr 03 2020 *)

Crossrefs

Cf. A001519.

Sequence in context: A005174 A034668 A215854 * A230390 A089832 A161170

Adjacent sequences: A123355 A123356 A123357 * A123359 A123360 A123361

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 10 2006

Status

approved