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Search: id:A116574
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| A116574 |
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A Binet type formula from a polynomial whose coefficient expansion gives a tribonacci used as it first derivative InverseZtransform: A000073. |
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+0
1
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| 0, 1, 10, 1, 49, 225, 36, 730, 4097, 2025, 4761, 48401, 46225, 13456, 432965, 703922, 1, 3066002, 8185321, 1134225, 16974401, 78145601, 35545444, 67043345, 632572802
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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x^2/(1 - x - x^2 - x^3) is similar to the polynomial: -(x/(x^3 + x^2 + x - 1)) but not the same. As the last is machine derived, it is probly more correct than the one quoted presently in A000072.
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FORMULA
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(*Source : A000073*) g[x_] = x^2/(1 - x - x^2 - x^3); dg[x_] = D[g[x], {x, 1}]; w[n_] := InverseZTransform[dg[x], x, n] // ToRadicals; a(n) =Abs[w[n]]^2
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MATHEMATICA
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(*Source : A000073*) g[x_] = x^2/(1 - x - x^2 - x^3); dg[x_] = D[g[x], {x, 1}]; w[n_] := InverseZTransform[dg[x], x, n] // ToRadicals; Table[Abs[Floor[N[w[n]]]]^2, {n, 1, 25}]
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CROSSREFS
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Cf. A000073.
Sequence in context: A059022 A115097 A050313 this_sequence A049326 A146537 A050304
Adjacent sequences: A116571 A116572 A116573 this_sequence A116575 A116576 A116577
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KEYWORD
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nonn,uned,probation,obsc
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 19 2006
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