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Search: id:A118587
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| A118587 |
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A nested recursion from a cubic prime generating polynomial so that only the ending coefficients are necessary to determine the recursion: f[x_] = 17*x^3 - 62*x^2 + 71*x + 17. |
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| 17, 43, 47, 131, 397, 947, 1883, 3307, 5321, 8027, 11527, 15923, 21317, 27811, 35507, 44507, 54913, 66827, 80351, 95587, 112637, 131603, 152587, 175691, 201017, 228667, 258743, 291347, 326581, 364547, 405347, 449083, 495857, 545771, 598927
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The polynomials from the recursions form a limited triangular tree. An infinite polynomial would in this same way make an infinite nested recursion in analog to a continued fraction.
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FORMULA
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d[n_] := d[n] = d[n - 1] + 102 c[n_] := c[n] = c[n - 1] + d[n] b[n_] := b[n] = b[n - 1] + c[n] a(n) = a(n-1)+b[n]
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EXAMPLE
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102
-226 + 102 n
150 - 175 n + 51 n^2
17 + 71 n + 62 n^2 +17 n^3
So {17, 150, -226, 102} determine the nested recursions.
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CROSSREFS
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Sequence in context: A044475 A024188 A086006 this_sequence A123592 A109998 A031340
Adjacent sequences: A118584 A118585 A118586 this_sequence A118588 A118589 A118590
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KEYWORD
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nonn,uned,obsc
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), May 06 2006
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