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Search: id:A121954
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| A121954 |
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Binet version of recursion sequence a[n] = (n + 1)*a[n - 1] + a[n - 2]: closely related to A001053. |
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1
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| 0, 1, 3, 13, 68, 420, 3015, 24541, 223884, 2263381, 25121075, 303716281, 3973432728, 55931774473, 842950049823, 13543132571641, 231076203767720, 4172914800390601, 79516457411189152, 1594502063024173568
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Using Bob Hanlon's Fibonascci Binet solver in Mathematica, I get a new Bessel function solution for a sequence similar in form to A001053. As far as I know this is an entirely new machine generated soluution to this type of problem.
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FORMULA
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a(n) = (BesselI[2 + n, -2] BesselK[2, 2] - BesselI[2, -2] BesselK[2 + n, 2])/(BesselI[3, -2] BesselK[2, 2] - BesselI[2, -2] BesselK[3, 2])
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MATHEMATICA
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Needs["DiscreteMath`RSolve`"]; Clear[f]; f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == (n + 1)*a[n - 1] + a[n - 2], a[0] == 0, a[1] == 1}, a[n], n][[1]] // Simplify] // ToRadicals Table[Floor[N[f[n]]], {n, 0, 25}]
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CROSSREFS
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Cf. A001053.
Sequence in context: A047149 A000260 A125279 this_sequence A058307 A020107 A128079
Adjacent sequences: A121951 A121952 A121953 this_sequence A121955 A121956 A121957
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 01 2006
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