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A191891
Ordered sums 4*f+5*g, where f and g are positive Fibonacci numbers (A000045).
4
9, 13, 14, 17, 18, 19, 22, 23, 25, 27, 29, 30, 33, 35, 37, 42, 44, 45, 47, 48, 52, 57, 60, 62, 67, 69, 72, 73, 77, 85, 89, 92, 94, 97, 99, 109, 113, 117, 124, 125, 137, 141, 146, 149, 151, 157, 161, 174, 176, 178, 182, 189, 190, 201, 202, 222, 225, 230, 235
OFFSET
1,1
LINKS
MAPLE
F:= [seq(combinat:-fibonacci(n), n=2..20)]:
N:= 4*F[-1]+5:
sort(select(`<=`, convert({seq(seq(4*f+5*g, g=F), f=F)}, list), N)); # Robert Israel, Apr 06 2017
MATHEMATICA
c = 4; d = 5; f[n_] := Fibonacci[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 ]] (* A191891 *)
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 ]] (* A191892: 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 ]] (* A191893: d*f(i)-c*f(j) *)
v3 = Union[v1, v2] (* A191894*)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 18 2011
EXTENSIONS
Name improved by Robert Israel, Apr 06 2017
STATUS
approved