A395228 - OEIS

%I #9 May 04 2026 19:47:12

%S 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,

%T 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,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%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 < y < z.

%e a(17) = 1 counts this 4-tuple: (1,2,3,5).

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

%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, 17, 160}]];

%t Map[Length, t]

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

%Y Cf. A395226, A395227, A395229, A395230.

%K nonn

%O 17

%A _Clark Kimberling_, Apr 24 2026