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A108682 a(n) = (n+1)*(n+2)^2*(n+3)*(n+4)*(4*n^2+15*n+15)/720. 1
1, 17, 122, 560, 1946, 5586, 13944, 31284, 64515, 124267, 226226, 392756, 654836, 1054340, 1646688, 2503896, 3718053, 5405253, 7710010, 10810184, 14922446, 20308310, 27280760, 36211500, 47538855, 61776351, 79522002, 101468332, 128413160, 161271176, 201086336 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Kekulé numbers for certain benzenoids.

REFERENCES

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 233, # 7).

LINKS

Table of n, a(n) for n=0..30.

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

FORMULA

G.f.: (1 + 9z + 14z^2 + 4z^3)/(1-z)^8.

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). - Wesley Ivan Hurt, May 23 2015

MAPLE

A108682:=n->(n+1)*(n+2)^2*(n+3)*(n+4)*(4*n^2+15*n+15)/720: seq(A108682(n), n=0..50); # Wesley Ivan Hurt, May 23 2015

MATHEMATICA

Table[(n+1)(n+2)^2(n+3)(n+4)(4n^2+15n+15)/720, {n, 0, 40}] (* or *)

CoefficientList[Series[(1+9x+14x^2+4x^3)/(1-x)^8, {x, 0, 40}], x] (* Harvey P. Dale, Mar 28 2011 *)

PROG

(MAGMA) [(n+1)*(n+2)^2*(n+3)*(n+4)*(4*n^2+15*n+15)/720 : n in [0..50]]; // Wesley Ivan Hurt, May 23 2015

CROSSREFS

Sequence in context: A196806 A094944 A274325 * A031213 A196145 A021003

Adjacent sequences:  A108679 A108680 A108681 * A108683 A108684 A108685

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jun 18 2005

STATUS

approved

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)