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A122010
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G.f. x^2*(1-5*x)/(1-12*x+15*x^2-2*x^3).
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2
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0, 1, 7, 69, 725, 7679, 81411, 863197, 9152557, 97045551, 1028984651, 10910437661, 115684573269, 1226616283615, 13005947679667, 137903497048317, 1462205981952029, 15503931223058927, 164389891941523323
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OFFSET
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1,3
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COMMENTS
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Limit a(n+1)/a(n) = 10.6031 as n -> infinity.
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REFERENCES
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"Linear Algebra, Examples and Applications" by Alain M. Robert, World Scientific, 2005, p. 58.
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LINKS
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FORMULA
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a(n)= 12*a(n-1) -15*a(n-2) +2*a(n-3).
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MATHEMATICA
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M = {{1, 1, 1}, {1, 2, 4}, {1, 3, 9}} v[1] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] a1 = Table[v[n][[2]], {n, 1, 50}]
LinearRecurrence[{12, -15, 2}, {0, 1, 7}, 20] (* Harvey P. Dale, Mar 11 2022 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Definition replaced with generating function by the Assoc. Eds. of the OEIS, Mar 27 2010
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STATUS
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approved
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