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A124025
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Recursive polynomial from a tridiagonal matrix version of A123965: p(k, x) = ((x - b(k - 1))*p(k - 1, x) - a(k - 2) *p(k - 2, x))/a(n - 1); a(n)=-1;b(n)=3;.
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1
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1, 3, -1, 8, -6, 1, 21, -25, 9, -1, 55, -90, 51, -12, 1, 144, -300, 234, -86, 15, -1, 377, -954, 951, -480, 130, -18, 1, 987, -2939, 3573, -2305, 855, -183, 21, -1, 2584, -8850, 12707, -10008, 4740, -1386, 245, -24, 1, 6765, -26195, 43398, -40426, 23373, -8715, 2100, -316, 27, -1, 17711, -76500, 143682
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Joanne Dombrowski, Tridiagonal matrix representations of cyclic selfadjoint operators, Pacific J. Math. 114, no. 2 (1984), 325-334
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FORMULA
| Recursive polynomial from a tridiagonal matrix version of A123965 ( first number different): p(k, x) = ((x - b(k - 1))*p(k - 1, x) - a(k - 2)*p(k - 2, x))/a(n - 1); a(n)=-1;b(n)=3;
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MATHEMATICA
| b[k_] = 3; a[k_] = -1; p[0, x] = 1; p[1, x] = (x - b[1])/a[1]; p[k_, x_] := p[k, x] = ((x - b[k - 1])*p[k - 1, x] - a[k - 2]*p[k - 2, x])/a[k - 1]; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]
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CROSSREFS
| Cf. A101950, A104562, A123965.
Sequence in context: A103247 A030523 A123965 * A125662 A005295 A077897
Adjacent sequences: A124022 A124023 A124024 * A124026 A124027 A124028
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KEYWORD
| uned,sign
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 31 2006
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