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A205870 [s(k)-s(j)]/8, where the pairs (k,j) are given by A205867 and A205868, and s(k) denotes the (k+1)-st Fibonacci number.

%I A205870 #5 Mar 30 2012 18:58:12
%S A205870 1,2,1,4,11,17,29,18,47,36,18,76,72,123,199,198,197,322,305,522,521,
%T A205870 520,323,845,844,843,646,323,1368,1364,1292,2207,3582,3571,3553,3535,
%U A205870 5795,5778,5473,9378,9367,9349,9331,5796,15174,15163,15145,15127
%N A205870 [s(k)-s(j)]/8, where the pairs (k,j) are given by A205867 and A205868, and s(k) denotes the (k+1)-st Fibonacci number.
%C A205870 For a guide to related sequences, see A205840.
%e A205870 The first six terms match these differences:
%e A205870 s(6)-s(4) = 13-5 = 8 = 8*1
%e A205870 s(7)-s(4) = 21-5 = 16 = 8*2
%e A205870 s(7)-s(6) = 21-13 = 8 = 8*1
%e A205870 s(8)-s(2) = 34-2 = 32 = 8*4
%e A205870 s(10)-s(1) = 89-1 = 88 = 8*11
%e A205870 s(11)-s(5) = 144-8 = 136 =8*17
%t A205870 s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
%t A205870 f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
%t A205870 Table[s[n], {n, 1, 30}]
%t A205870 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A205870 Table[u[m], {m, 1, z1}] (* A204922 *)
%t A205870 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A205870 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A205870 d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
%t A205870 c = 8; t = d[c]    (* A205866 *)
%t A205870 k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
%t A205870 j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
%t A205870 Table[k[n], {n, 1, z2}]   (* A205867 *)
%t A205870 Table[j[n], {n, 1, z2}]     (* A205868 *)
%t A205870 Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205869 *)
%t A205870 Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205870 *)
%Y A205870 Cf. A204892, A205867, A205869.
%K A205870 nonn
%O A205870 1,2
%A A205870 _Clark Kimberling_, Feb 02 2012