|
%I #10 Mar 30 2012 18:57:33
%S 5,7,8,9,10,11,12,13,15,16,17,19,21,22,25,26,28,29,30,31,32,34,35,40,
%T 41,43,45,48,49,50,51,55,57,65,66,67,69,71,73,74,77,79,81,83,89,92,
%U 104,105,106,107,108,112,113,116,118,119,125,128,131,134,144,149
%N Ordered sums 2*f+3*g, where f and g are Fibonacci numbers (A000045).
%t c = 2; d = 3; f[n_] := Fibonacci[n];
%t g[n_] := c*f[n]; h[n_] := d*f[n];
%t t[i_, j_] := h[i] + g[j];
%t u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
%t v = Union[Flatten[u ]] (* A191846 *)
%t t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
%t u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
%t v1 = Union[Flatten[u1 ]] (* A191847: 2f(i)-3*f(j) *)
%t g1[n_] := d*f[n]; h1[n_] := c*f[n];
%t t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
%t u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
%t v2 = Union[Flatten[u2 ]] (* A191848: 3*f(i)-2(f(j) *)
%t v3 = Union[v1, v2] (* A191849 *)
%Y Cf. A191846, A191847, A191848.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jun 17 2011
|
