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A174988
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Expansion of -x*(x-1)*(3*x+1) / (9*x^4-8*x^2+1).
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0
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0, 1, 2, 5, 16, 31, 110, 203, 736, 1345, 4898, 8933, 32560, 59359, 216398, 394475, 1438144, 2621569, 9557570, 17422277, 63517264, 115784095, 422119982, 769472267, 2805304480, 5113721281, 18643356002, 33984519845, 123899107696
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OFFSET
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0,3
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COMMENTS
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Old name was: a(n)=2^Floor[n/2]*((1 + Sqrt[7])^n - (1 - Sqrt[7])^n)/(2^n*Sqrt[7]).
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REFERENCES
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Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.
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LINKS
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FORMULA
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a(n) = 8*a(n-2)-9*a(n-4). G.f.: -x*(x-1)*(3*x+1)/(9*x^4-8*x^2+1). [Colin Barker, Jan 05 2013]
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MATHEMATICA
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f[n_] = 2^Floor[n/2]*((1 + Sqrt[7])^n - (1 - Sqrt[7])^n)/(2^n*Sqrt[7]);
Table[FullSimplify[ExpandAll[f[n]]], {n, 0, 30}]
LinearRecurrence[{0, 8, 0, -9}, {0, 1, 2, 5}, 30] (* Harvey P. Dale, Aug 21 2014 *)
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PROG
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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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STATUS
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approved
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