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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
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).
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 18 2005
STATUS
approved