A395228 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 < y < z.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

17

Links

Table of n, a(n) for n=17..102.

Example

a(17) = 1 counts this 4-tuple: (1,2,3,5).
a(278) = 3 counts these 4-tuples: (1, 3, 5, 55), (1, 5, 12, 21), (2, 3, 8, 34).

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, 17, 160}]];
Map[Length, t]
(* Peter J. C. Moses, Apr 02 2026 *)

Crossrefs

Cf. A395226, A395227, A395229, A395230.

Sequence in context: A014954 A015899 A015494 * A267142 A373838 A185119

Adjacent sequences: A395225 A395226 A395227 * A395229 A395230 A395231

Keyword

nonn

Author

Clark Kimberling, Apr 24 2026

Status

approved