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Search: id:A116573
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| A116573 |
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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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1
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| 1, 0, 4, 17, 1, 82, 324, 49, 961, 5185, 2501, 5776, 57600, 54290, 15625, 497026, 801025, 1, 3437317, 9120400, 1256641, 18714277, 85766122, 38850289, 72999937
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OFFSET
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0,3
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COMMENT
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A polynomial derived in Mathematica by bob hanlon that is different than that in A000073 : first derivative sequence is different as well. Bob Hanlon's code: Needs["DiscreteMath`RSolve`"]; eqns={a[n]==a[n-1]+a[n-2]+a[n-3], a[0]==0,a[1]==a[2]==1}; Clear[f0,f1,f2,f3]; f0[0]=0;f0[1]=f0[2]=1; f0[n_Integer?Positive]:= f0[n]=f0[n-1]+f0[n-2]+f0[n-3]; f1[n_Integer]=a[n]/. RSolve[eqns,a[n],n][[1]]// ToRadicals//Simplify; (*Note that f1[n] is not restricted to nonnegative values of n.*) (*RSolve can also provide the generating function*) gf[x_]=GeneratingFunction[ eqns,a[n],n,x][[1,1]] -(x/(x^3 + x^2 + x - 1)) f2[n_Integer?NonNegative]:= SeriesCoefficient[ Series[gf[x],{x,0,n}],n];
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REFERENCES
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Private email from Bob Hanlon, (hanlonr(AT)cox.net), Mar 18 2006
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FORMULA
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g[x_] = -(x/(x^3 + x^2 + x - 1)); 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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g[x_] = -(x/(x^3 + x^2 + x - 1)); 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: A013001 A013179 A123234 this_sequence A063625 A057596 A070712
Adjacent sequences: A116570 A116571 A116572 this_sequence A116574 A116575 A116576
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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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