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

Author

N. J. A. Sloane, Oct 10 2006

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

Cf. A001519.

Programs

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 *)

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