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A191976
Ordered sums 3f+4g, where f and g are Lucas numbers (A000032 beginning at 1).
4
7, 13, 15, 16, 19, 21, 24, 25, 28, 31, 33, 37, 40, 45, 47, 49, 53, 56, 58, 61, 65, 66, 70, 75, 77, 81, 82, 84, 91, 93, 98, 99, 103, 105, 115, 119, 125, 126, 128, 131, 137, 145, 149, 153, 157, 159, 169, 170, 185, 191, 197, 200, 203, 209, 213, 221, 232, 240
OFFSET
1,1
MATHEMATICA
c = 3; d = 4; f[n_] := LucasL[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]] (* A191976 *)
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]] (*A 191977: c*f(i)-d*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]] (* A191978: d*f(i)-c*f(j) *)
v3 = Union[v1, v2] (* A191979 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 20 2011
STATUS
approved