A110694 Kekulé numbers for certain benzenoids.

1, 19, 142, 664, 2330, 6726, 16848, 37884, 78243, 150865, 274846, 477412, 796276, 1282412, 2003280, 3046536, 4524261, 6577743, 9382846, 13156000, 18160846, 24715570, 33200960, 44069220, 57853575, 75178701, 96772014, 123475852

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 243, M_n(LLLAALL)).

Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Formula

a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(34*n^3 + 199*n^2 + 355*n + 210)/7!.

a(0)=1, a(1)=19, a(2)=142, a(3)=664, a(4)=2330, a(5)=6726, a(6)=16848, a(7)=37884, a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Harvey P. Dale, Feb 16 2014

G.f.: (1 + 11*x + 18*x^2 + 4*x^3)/(1 - x)^8. - G. C. Greubel, Sep 06 2017

Maple

a:=n->(n+1)*(n+2)*(n+3)*(n+4)*(34*n^3+199*n^2+355*n+210)/5040: seq(a(n), n=0..31);

Mathematica

Table[(n+1)(n+2)(n+3)(n+4)(34n^3+199n^2+355n+210)/5040, {n, 0, 30}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 19, 142, 664, 2330, 6726, 16848, 37884}, 30] (* Harvey P. Dale, Feb 16 2014 *)

Prog

(Magma) [(n+1)*(n+2)*(n+3)*(n+4)*(34*n^3+199*n^2+355*n+210)/5040: n in [0..30]]; // Vincenzo Librandi, Mar 28 2012
(PARI) x='x+O('x^50); Vec((1 + 11*x + 18*x^2 + 4*x^3)/(1 - x)^8) \\ G. C. Greubel, Sep 06 2017

Crossrefs

Sequence in context: A060104 A201151 A221600 * A107962 A002615 A081590

Adjacent sequences: A110691 A110692 A110693 * A110695 A110696 A110697

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 03 2005

Status

approved