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A110694 Kekulé numbers for certain benzenoids. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 15:59 EST 2022. Contains 358468 sequences. (Running on oeis4.)