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A191920 Ordered sums f+3*g, where f and g are Lucas numbers (A000032 beginning at 1).

%I A191920 #12 Jun 19 2025 09:20:05
%S A191920 4,6,7,10,12,13,14,15,16,19,20,21,22,23,24,25,27,28,30,32,34,36,37,38,
%T A191920 39,40,41,44,50,51,55,56,57,58,59,61,62,65,68,72,79,80,83,85,88,90,91,
%U A191920 94,97,98,101,105,109,116,126,130,132,134,135,142,144,145
%N A191920 Ordered sums f+3*g, where f and g are Lucas numbers (A000032 beginning at 1).
%t A191920 c = 1; d = 3; f[n_] := LucasL[n];
%t A191920 g[n_] := c*f[n]; h[n_] := d*f[n];
%t A191920 t[i_, j_] := h[i] + g[j];
%t A191920 u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191920 v = Union[Flatten[u]]    (* A191920 *)
%t A191920 t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
%t A191920 u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191920 v1 = Union[Flatten[u1]]  (* A191921: c*f(i)-d*f(j) *)
%t A191920 g1[n_] := d*f[n]; h1[n_] := c*f[n];
%t A191920 t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
%t A191920 u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191920 v2 = Union[Flatten[u2]]  (* A191922: d*f(i)-c*f(j) *)
%t A191920 v3 = Union[v1, v2]       (* A191923 *)
%Y A191920 Cf. A000032, A191921, A191922, A191923, A191842.
%K A191920 nonn
%O A191920 1,1
%A A191920 _Clark Kimberling_, Jun 19 2011