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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.

%I A205875 #6 Mar 30 2012 18:58:12
%S A205875 2,6,9,25,16,41,32,16,64,176,287,281,464,642,1216,1967,1958,1942,1926,
%T A205875 3184,3178,2897,5136,8336,8330,8049,5152,13488,13482,13201,10304,5152,
%U A205875 21824,20608,35312,35310,57136,56672,92448,92439,92423,92407
%N 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.
%C A205875 For a guide to related sequences, see A205840.
%e A205875 The first six terms match these differences:
%e A205875 s(7)-s(3) = 21-3 = 18 = 9*2
%e A205875 s(9)-s(1) = 55-1 = 54 = 9*6
%e A205875 s(10)-s(5) = 89-8 = 81 = 9*9
%e A205875 s(12)-s(5) = 233-8 = 225 = 9*25
%e A205875 s(12)-s(10) = 233-89 = 144 = 9*16
%e A205875 s(13)-s(5) = 377-8 = 369 =9*41
%t A205875 s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
%t A205875 f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
%t A205875 Table[s[n], {n, 1, 30}]
%t A205875 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A205875 Table[u[m], {m, 1, z1}]   (* A204922 *)
%t A205875 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A205875 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A205875 d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
%t A205875 c = 9; t = d[c]     (* A205871 *)
%t A205875 k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
%t A205875 j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
%t A205875 Table[k[n], {n, 1, z2}]       (* A205872 *)
%t A205875 Table[j[n], {n, 1, z2}]         (* A205873 *)
%t A205875 Table[s[k[n]] - s[j[n]], {n, 1, z2}]   (* A205874 *)
%t A205875 Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205875 *)
%Y A205875 Cf. A204892, A205872, A205874.
%K A205875 nonn
%O A205875 1,1
%A A205875 _Clark Kimberling_, Feb 02 2012