|
|
A116574
|
|
A Binet type formula from a polynomial whose coefficient expansion gives a tribonacci used as it first derivative InverseZtransform: A000073.
|
|
0
|
|
|
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;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,uned,obsc
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|