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A205875
[s(k)-s(j)]/9, where the pairs (k,j) are given by A205872 and A205873, and s(k) denotes the (k+1)-st Fibonacci number.
3
2, 6, 9, 25, 16, 41, 32, 16, 64, 176, 287, 281, 464, 642, 1216, 1967, 1958, 1942, 1926, 3184, 3178, 2897, 5136, 8336, 8330, 8049, 5152, 13488, 13482, 13201, 10304, 5152, 21824, 20608, 35312, 35310, 57136, 56672, 92448, 92439, 92423, 92407
OFFSET
1,1
COMMENTS
For a guide to related sequences, see A205840.
EXAMPLE
The first six terms match these differences:
s(7)-s(3) = 21-3 = 18 = 9*2
s(9)-s(1) = 55-1 = 54 = 9*6
s(10)-s(5) = 89-8 = 81 = 9*9
s(12)-s(5) = 233-8 = 225 = 9*25
s(12)-s(10) = 233-89 = 144 = 9*16
s(13)-s(5) = 377-8 = 369 =9*41
MATHEMATICA
s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}] (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 9; t = d[c] (* A205871 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}] (* A205872 *)
Table[j[n], {n, 1, z2}] (* A205873 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205874 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205875 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 02 2012
STATUS
approved