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A120333
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Number of monocyclic skeletons with n carbon atoms and a ring size of 5.
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3
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1, 1, 4, 9, 28, 71, 198, 521, 1418, 3773, 10153, 27114, 72705, 194531, 521447, 1397482, 3749836, 10067417, 27057233, 72779710, 195963184, 528127752, 1424707167, 3846943003, 10397057771, 28125235102, 76149287981, 206351312858, 559642013499, 1519019192097
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OFFSET
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5,3
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REFERENCES
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Camden A. Parks and James B. Hendrickson, Enumeration of monocyclic and bicyclic carbon skeletons, J. Chem. Inf. Comput. Sci., vol. 31, 334-339 (1991).
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LINKS
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EXAMPLE
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If n=10 then the number of monocyclic skeletons with ring size of five is 71.
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MATHEMATICA
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G[n_] := Module[{g}, Do[g[x_] = 1 + x*(g[x]^3/6 + g[x^2]*g[x]/2 + g[x^3]/3) + O[x]^n // Normal, {n}]; g[x]];
T[n_, k_] := Module[{t = G[n], g}, t = x*((t^2 + (t /. x -> x^2))/2); g[e_] = (Normal[t + O[x]^Quotient[n, e]] /. x -> x^e) + O[x]^n // Normal; Coefficient[(Sum[EulerPhi[d]*g[d]^(k/d), {d, Divisors[k]}]/k + If[OddQ[ k], g[1]*g[2]^Quotient[k, 2], (g[1]^2 + g[2])*g[2]^(k/2-1)/2])/2, x, n]];
a[n_] := T[n + 5, 5];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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