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A191976 Ordered sums 3*f+4*g, where f and g are Lucas numbers (A000032 beginning at 1).

%I A191976 #8 Jun 19 2025 20:56:09
%S A191976 7,13,15,16,19,21,24,25,28,31,33,37,40,45,47,49,53,56,58,61,65,66,70,
%T A191976 75,77,81,82,84,91,93,98,99,103,105,115,119,125,126,128,131,137,145,
%U A191976 149,153,157,159,169,170,185,191,197,200,203,209,213,221,232,240
%N A191976 Ordered sums 3*f+4*g, where f and g are Lucas numbers (A000032 beginning at 1).
%t A191976 c = 3; d = 4; f[n_] := LucasL[n];
%t A191976 g[n_] := c*f[n]; h[n_] := d*f[n];
%t A191976 t[i_, j_] := h[i] + g[j];
%t A191976 u = Table[t[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191976 v = Union[Flatten[u]]    (* A191976 *)
%t A191976 t1[i_, j_] := If[g[i] - h[j] > 0, g[i] - h[j], 0]
%t A191976 u1 = Table[t1[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191976 v1 = Union[Flatten[u1]]  (* A191977: c*f(i)-d*f(j) *)
%t A191976 g1[n_] := d*f[n]; h1[n_] := c*f[n];
%t A191976 t2[i_, j_] := If[g1[i] - h1[j] > 0, g1[i] - h1[j], 0]
%t A191976 u2 = Table[t2[i, j], {i, 1, 20}, {j, 1, 20}];
%t A191976 v2 = Union[Flatten[u2]]  (* A191978: d*f(i)-c*f(j) *)
%t A191976 v3 = Union[v1, v2]       (* A191979 *)
%Y A191976 Cf. A191977, A191978, A191979, A191929.
%K A191976 nonn
%O A191976 1,1
%A A191976 _Clark Kimberling_, Jun 20 2011