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A114241
a(n) = (n+1)*(n+2)*(n+3)*(11*n^2 + 29*n + 20)/120.
1
1, 12, 61, 206, 546, 1232, 2478, 4572, 7887, 12892, 20163, 30394, 44408, 63168, 87788, 119544, 159885, 210444, 273049, 349734, 442750, 554576, 687930, 845780, 1031355, 1248156, 1499967, 1790866, 2125236, 2507776, 2943512, 3437808
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. 168).
FORMULA
From Chai Wah Wu, Nov 11 2018: (Start)
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 5.
G.f.: (4*x^2 + 6*x + 1)/(x - 1)^6. (End)
E.g.f.: (120 + 1320*x + 2280*x^2 + 1160*x^3 + 205*x^4 + 11*x^5)*exp(x)/5!. - G. C. Greubel, Nov 11 2018
MAPLE
a:=n->(n+1)*(n+2)*(n+3)*(11*n^2+29*n+20)/120: seq(a(n), n=0..38);
MATHEMATICA
Table[Binomial[n+3, 3]*(11*n^2 +29*n +20)/20, {n, 0, 20}] (* G. C. Greubel, Nov 11 2018 *)
PROG
(PARI) vector(35, n, n--; binomial(n+3, 3)*(11*n^2 +29*n +20)/20) \\ G. C. Greubel, Nov 11 2018
(Magma) [Binomial(n+3, 3)*(11*n^2 +29*n +20)/20: n in [0..35]]; // G. C. Greubel, Nov 11 2018
CROSSREFS
Sequence in context: A044531 A304205 A240002 * A127766 A005173 A196144
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 18 2005
STATUS
approved