A116574 - OEIS

%I #8 Aug 02 2013 16:21:38

%S 0,1,10,1,49,225,36,730,4097,2025,4761,48401,46225,13456,432965,

%T 703922,1,3066002,8185321,1134225,16974401,78145601,35545444,67043345,

%U 632572802

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

%C 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.

%F (*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

%t (*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}]

%Y Cf. A000073.

%K nonn,uned,obsc

%O 0,3

%A _Roger L. Bagula_, Mar 19 2006