A191842 Ordered sums f+3*g, where f and g are Fibonacci numbers (A000045).

4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 36, 37, 40, 41, 42, 43, 44, 45, 47, 49, 52, 58, 60, 61, 64, 65, 66, 68, 70, 71, 73, 76, 79, 84, 92, 94, 95, 97, 98, 103, 104, 105, 107, 110, 113, 115, 118, 123, 128

Offset: 1

Author

Clark Kimberling, Jun 17 2011

Keywords

• nonn

Crossrefs

Cf. A191843, A191844, A191845.

Programs

Mathematica

c = 1; d = 3; f[n_] := Fibonacci[n];
g[n_] := c*f[n]; h[n_] := d*f[n];
t[i_, j_] := h[i] + g[j];
u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
v = Union[Flatten[u ]]    (* A191842 *)
t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
v1 = Union[Flatten[u1 ]]  (* A191843: f(i)-3*f(j) *)
g1[n_] := d*f[n]; h1[n_] := c*f[n];
t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
v2 = Union[Flatten[u2 ]]  (* A191844: 3*f(i)-f(j) *)
v3 = Union[v1, v2]        (* A191845 *)