A395227 - OEIS

%I #11 May 02 2026 15:53:43

%S 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,

%T 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,

%U 9,2,6,8,0,8,4,2,8,0,7,6,3,8,2,2,5,0

%N 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.

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

%t fQ[n_] := fQ[n] = IntegerQ[Sqrt[5 n^2 + 4]] || IntegerQ[Sqrt[5 n^2 - 4]];

%t f[n_] := f[n] = Map[{#, n/#} &, Select[Divisors[n], # <= n/# &]];

%t 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 t = Join[{0},Table[Select[s[n], AllTrue[#, fQ] && #[[1]] < #[[2]] && #[[3]] < #[[4]] &], {n, 1, 160}]];

%t Map[Length, t]

%t (* _Peter J. C. Moses_, Apr 02 2026 *)

%Y Cf. A395226, A395228, A395229, A395230.

%K nonn

%O 0,6

%A _Clark Kimberling_, Apr 24 2026