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A120711
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7 X 7 matrix Matrov of seven vertex Fano Plane: Characteristic polynomial : 12 + 10 x - 24 x^2 - 21 x^3 + 12 x^4 + 12 x^5 - x^7.
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0
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0, 14, 32, 150, 492, 1894, 6724, 24854, 89972, 329238, 1197972, 4372054, 15930580, 58096214, 211770452, 772129110, 2814859092, 10262536534, 37414140244, 136403674454, 497291840852, 1813006427478, 6609762501972, 24097566365014
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OFFSET
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0,2
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COMMENTS
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Limited here to seven connecting lines in the bonding graph.
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REFERENCES
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(*http://mathworld.wolfram.com/FanoPlane.html*)
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LINKS
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Table of n, a(n) for n=0..23.
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FORMULA
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M = {{0, 1, 0, 0, 0, 1, 1}, {1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 0, 1}, {0, 0, 1, 0, 1, 0, 1}, {0, 0, 0, 1, 0, 1, 1}, {1, 0, 0, 0, 1, 0, 1}, {1, 1, 1, 1, 1, 1, 0}} v[1] = {0, 1, 1, 2, 3, 5, 8} v[n_] := v[n] = M.v[n - 1] a(n) =v[n][[1]].
Empirical G.f.: 2*x*(7+16*x-2*x^2-14*x^3)/((1-x)*(1+x)*(1+2*x)*(1-2*x-6*x^2)). [Colin Barker, Mar 26 2012]
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MATHEMATICA
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M = {{0, 1, 0, 0, 0, 1, 1}, {1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 0, 1}, {0, 0, 1, 0, 1, 0, 1}, {0, 0, 0, 1, 0, 1, 1}, {1, 0, 0, 0, 1, 0, 1}, {1, 1, 1, 1, 1, 1, 0}} v[1] = {0, 1, 1, 2, 3, 5, 8} v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
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Cf. A111384.
Sequence in context: A084194 A031109 A155819 * A018959 A225420 A107484
Adjacent sequences: A120708 A120709 A120710 * A120712 A120713 A120714
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula, Aug 12 2006
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STATUS
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approved
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