A203697 Vandermonde sequence using x^2 + xy + y^2 applied to the Fibonacci numbers (1,2,3,5,...F(n+1)).

1, 7, 1729, 102427689, 7859247487506324, 5420939118751361437801775388, 212771631278201852610030565508935087592924796, 3245346956445033097411208139940145810977419605290236367412235927744

Offset: 1

Author

Clark Kimberling, Jan 04 2012

Keywords

• nonn

Comments

See A093883 for a discussion and guide to related sequences.

Programs

Mathematica

f[j_] := Fibonacci[j + 1]; z = 11;
u[n_] := Product[f[j]^2 + f[j] f[k] + f[k]^2,
  {j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203697 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203698 *)