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A205855 [s(k)-s(j)]/5, where the pairs (k,j) are given by A205852 and A205853, and s(k) denotes the (k+1)-st Fibonacci number.

%I A205855 #5 Mar 30 2012 18:58:12
%S A205855 1,2,1,4,10,11,22,11,46,45,44,75,121,111,197,122,319,244,122,510,499,
%T A205855 488,836,832,1352,1342,1231,2189,2185,1353,3542,3538,2706,1353,5731,
%U A205855 5656,5534,5412,9273,9272,9271,9227,15004,14994,14883,13652
%N A205855 [s(k)-s(j)]/5, where the pairs (k,j) are given by A205852 and A205853, and s(k) denotes the (k+1)-st Fibonacci number.
%C A205855 For a guide to related sequences, see A205840.
%e A205855 The first six terms match these differences:
%e A205855 s(5)-s(3) = 8-3 = 5 = 5*1
%e A205855 s(6)-s(3) = 13-3 = 10 = 5*2
%e A205855 s(6)-s(5) = 13-8 = 5 = 5*1
%e A205855 s(7)-s(1) = 21-1 = 20 = 5*4
%e A205855 s(9)-s(4) = 55-5 = 50 = 5*10
%e A205855 s(10)-s(8) = 89-34 = 55 =5*11
%t A205855 s[n_] := s[n] = Fibonacci[n + 1]; z1 = 500; z2 = 60;
%t A205855 f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
%t A205855 Table[s[n], {n, 1, 30}]
%t A205855 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A205855 Table[u[m], {m, 1, z1}]    (* A204922 *)
%t A205855 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A205855 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A205855 d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
%t A205855 c = 5; t = d[c]    (* A205851 *)
%t A205855 k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
%t A205855 j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
%t A205855 Table[k[n], {n, 1, z2}]   (* A205852 *)
%t A205855 Table[j[n], {n, 1, z2}]   (* A205853 *)
%t A205855 Table[s[k[n]]-s[j[n]], {n,1,z2}] (* A205854 *)
%t A205855 Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205855 *)
%Y A205855 Cf. A204892, A205852, A205854.
%K A205855 nonn
%O A205855 1,2
%A A205855 _Clark Kimberling_, Feb 02 2012