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A038392
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Number of mono-4-polyhexes with n cells.
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4
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1, 1, 2, 6, 19, 71, 274, 1117, 4650, 19819, 85710, 375712, 1664203, 7439593, 33515758, 152019560, 693625265, 3181528275, 14661581030, 67850297506, 315187646601, 1469195636293, 6869889703638, 32215399021901, 151467334017864, 713881817440421, 3372142139764434
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OFFSET
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1,3
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REFERENCES
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J. Brunvoll, B. N. Cyvin, and S. J. Cyvin, Studies of some chemically relevant polygonal systems: mono-q-polyhexes, ACH Models in Chem., 133 (3) (1996), 277-298; see Eq. 16.
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LINKS
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Eric Weisstein's World of Mathematics, Fusene.
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FORMULA
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G.f.: (2(1-z^2) - (1-z)f(z) - f(z^2))/(4(1-z)) where f(z) = sqrt(1-6z+5z^2). - Emeric Deutsch, Mar 14 2004
(250*n^2-250*n)*a(n)+(-300*n^2-150*n)*a(n+1)+(-325*n^2-875*n-600)*a(n+2)+(475*n^2+2045*n+2100)*a(n+3)+(35*n^2+265*n+540)*a(n+4)+(-193*n^2-1691*n-3660)*a(n+5)+(49*n^2+563*n+1596)*a(n+6)+(17*n^2+211*n+648)*a(n+7)+(-9*n^2-135*n-504)*a(n+8)+(n^2+17*n+72)*a(n+9) = 0. - Robert Israel, Oct 08 2017
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MAPLE
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f:= gfun:-rectoproc({(250*n^2-250*n)*a(n)+(-300*n^2-150*n)*a(n+1)+(-325*n^2-875*n-600)*a(n+2)+(475*n^2+2045*n+2100)*a(n+3)+(35*n^2+265*n+540)*a(n+4)+(-193*n^2-1691*n-3660)*a(n+5)+(49*n^2+563*n+1596)*a(n+6)+(17*n^2+211*n+648)*a(n+7)+(-9*n^2-135*n-504)*a(n+8)+(n^2+17*n+72)*a(n+9), a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2, a(4) = 6, a(5) = 19, a(6) = 71, a(7) = 274, a(8) = 1117}, a(n), remember):
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MATHEMATICA
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f[z_] := Sqrt[5*z^2 - 6*z + 1]; g[z_] := (2*(1 - z^2) - (1-z)*f[z] - f[z^2])/ (4*(1-z)); Drop[ CoefficientList[ Series[ g[z], {z, 0, 24}], z], 1] (* Jean-François Alcover, Oct 13 2011, after Emeric Deutsch *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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