A116574 A Binet type formula from a polynomial whose coefficient expansion gives a tribonacci used as it first derivative InverseZtransform: A000073.

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

Offset

0,3

Comments

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 probably more correct than the one quoted presently in A000073.

Links

Table of n, a(n) for n=0..24.

Formula

(*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

Mathematica

(*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}]

Crossrefs

Cf. A000073.

Sequence in context: A193634 A115097 A050313 * A049326 A146537 A050304

Adjacent sequences: A116571 A116572 A116573 * A116575 A116576 A116577

Keyword

nonn,uned,obsc

Author

Roger L. Bagula, Mar 19 2006

Status

approved