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A205880 [s(k)-s(j)]/10, where the pairs (k,j) are given by A205877 and A205878, and s(k) denotes the (k+1)-st Fibonacci number.

%I A205880 #5 Mar 30 2012 18:58:12
%S A205880 1,2,5,11,23,22,61,122,61,255,244,418,416,676,671,1771,1769,1353,2828,
%T A205880 2767,2706,4636,7502,7497,6826,12139,12138,12116,19641,15005,31781,
%U A205880 31779,31363,30010,51414,83143,134618,83204,217822,166408,83204
%N A205880 [s(k)-s(j)]/10, where the pairs (k,j) are given by A205877 and A205878, and s(k) denotes the (k+1)-st Fibonacci number.
%C A205880 For a guide to related sequences, see A205840.
%e A205880 The first three terms match these differences:
%e A205880 s(6)-s(3) = 13-3 = 10 = 10*1
%e A205880 s(7)-s(1) = 21-1 = 20 = 10*2
%e A205880 s(9)-s(4) = 55-5 = 50 = 10*5
%t A205880 s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
%t A205880 f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
%t A205880 Table[s[n], {n, 1, 30}]
%t A205880 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A205880 Table[u[m], {m, 1, z1}]  (* A204922 *)
%t A205880 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A205880 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A205880 d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
%t A205880 c = 10; t = d[c]    (* A205876 *)
%t A205880 k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
%t A205880 j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
%t A205880 Table[k[n], {n, 1, z2}]   (* A205877 *)
%t A205880 Table[j[n], {n, 1, z2}]   (* A205878 *)
%t A205880 Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205879 *)
%t A205880 Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205880 *)
%Y A205880 Cf. A204892, A205877, A205879.
%K A205880 nonn
%O A205880 1,2
%A A205880 _Clark Kimberling_, Feb 02 2012