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Search: id:A121354
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| A121354 |
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An A053984-like Bessel-Binet recursion found by Bob Hanlon's new survey program: a[n] = (3*n - 1)*a[n - 1] - a[n - 2]. |
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1
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| 0, 1, 5, 39, 424, 5897, 99825, 1990603, 45684044, 1185794541, 34342357645, 1097769650099, 38387595395820, 1457630855391061, 59724477475637681, 2626419378072666903, 123381986291939706760, 6166472895218912671097
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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I had theorized that there were a related kind of Bessel-Binets of the form: a[n]=(a0*n+c0)*a[n-1]+b0*a[n-2] Where the a0,b0 and c0 were Integers. Bob Hanlon found ones with a0=2 in a program he wrote. A053984 was already in OEIS. This one is a0=3
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FORMULA
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a(n) = (3*n + 1)*a(n - 1) - a(n - 2) a(n)=(1/3) pi BesselJ[2/3 + n, 2/3] BesselY[2/3, 2/3] - (1/3) pi BesselJ[2/3, 2/3] BesselY[2/3 + n, 2/3]
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MATHEMATICA
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f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == (3*n - 1)*a[n - 1] - a[n - 2], a[0] == 0, a[1] == 1}, a[n], n][[1]] // FullSimplify] Rationalize[N[Table[f[n], {n, 0, 25}], 100], 0]
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CROSSREFS
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Cf. A053984, A001503.
Adjacent sequences: A121351 A121352 A121353 this_sequence A121355 A121356 A121357
Sequence in context: A124549 A024216 A127189 this_sequence A122486 A118991 A029538
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula and Bob Hanlon (rlbagulatftn(AT)yahoo.com), Sep 05 2006
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