A395227 a(n) = number of 4-tuples (w, x, y, z) such that w*x + y*z = n, where w, x, y, z are positive Fibonacci numbers satisfying w < x and y < z.

0, 0, 0, 0, 1, 2, 1, 2, 4, 2, 3, 4, 3, 4, 2, 4, 5, 2, 8, 4, 3, 6, 2, 6, 4, 2, 7, 4, 4, 8, 3, 6, 5, 0, 6, 0, 6, 6, 0, 6, 4, 4, 9, 2, 6, 8, 2, 8, 5, 4, 8, 0, 5, 2, 2, 8, 2, 4, 6, 0, 6, 4, 0, 6, 2, 6, 6, 2, 9, 2, 6, 8, 0, 8, 4, 2, 8, 0, 7, 6, 3, 8, 2, 2, 5, 0

Offset

0,6

Links

Table of n, a(n) for n=0..85.

Example

a(8) = 4 counts these 4-tuples: (1, 2, 2, 3), (1, 3, 1, 5), (1, 5, 1, 3), (2, 3, 1, 2).

Mathematica

fQ[n_] := fQ[n] = IntegerQ[Sqrt[5 n^2 + 4]] || IntegerQ[Sqrt[5 n^2 - 4]];
f[n_] := f[n] = Map[{#, n/#} &, Select[Divisors[n], # <= n/# &]];
s[n_] := Cases[Flatten[Table[Tuples[{f[k], f[n - k]}], {k, 1, n - 1}], 1], {{w_, x_}, {y_, z_}} :> {w, x, y, z}];
t = Join[{0}, Table[Select[s[n], AllTrue[#, fQ] && #[[1]] < #[[2]] && #[[3]] < #[[4]] &], {n, 1, 160}]];
Map[Length, t]
(* Peter J. C. Moses, Apr 02 2026 *)

Crossrefs

Cf. A395226, A395228, A395229, A395230.

Sequence in context: A184990 A206299 A276053 * A117268 A361076 A279709

Adjacent sequences: A395224 A395225 A395226 * A395228 A395229 A395230

Keyword

nonn

Author

Clark Kimberling, Apr 24 2026

Status

approved