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A191916 Ordered sums f+2g, where f and g are Lucas numbers (A000032 beginning at 1).

%I A191916 #7 Mar 30 2012 18:57:33
%S A191916 3,5,6,7,9,10,11,12,13,15,17,18,19,20,21,23,24,25,26,29,31,32,33,35,
%T A191916 37,39,40,43,47,49,51,53,54,55,59,61,62,65,69,76,78,82,83,84,87,90,95,
%U A191916 97,98,101,105,112,123,125,129,131,134,137,141,145,153,155
%N A191916 Ordered sums f+2g, where f and g are Lucas numbers (A000032 beginning at 1).
%t A191916 c = 1; d = 2; f[n_] := LucasL[n];
%t A191916 g[n_] := c*f[n]; h[n_] := d*f[n];
%t A191916 t[i_, j_] := h[i] + g[j];
%t A191916 u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191916 v = Union[Flatten[u ]]    (* A191916 *)
%t A191916 t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
%t A191916 u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191916 v1 = Union[Flatten[u1 ]]  (* A191917: c*f(i)-d*f(j) *)
%t A191916 g1[n_] := d*f[n]; h1[n_] := c*f[n];
%t A191916 t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
%t A191916 u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191916 v2 = Union[Flatten[u2 ]]  (* A191918: d*f(i)-c*f(j) *)
%t A191916 v3 = Union[v1, v2]         (* A191919*)
%Y A191916 Cf. A191917, A191918, A191919, A191838.
%K A191916 nonn
%O A191916 1,1
%A A191916 _Clark Kimberling_, Jun 19 2011