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%I #5 Mar 30 2012 18:58:12
%S 1,2,3,9,7,14,38,24,62,48,24,96,164,161,266,264,257,425,329,696,682,
%T 658,634,1127,1124,963,1824,1823,2951,2937,2913,2889,2255,4776,4774,
%U 4767,4510,7704,12504,12502,12495,12238,7728,20232,20230,20223
%N [s(k)-s(j)]/6, where the pairs (k,j) are given by A205857 and A205858, and s(k) denotes the (k+1)-st Fibonacci number.
%C For a guide to related sequences, see A205840.
%e The first six terms match these differences:
%e s(5)-s(2) = 8-2 = 6 = 6*1
%e s(6)-s(1) = 13-1 = 12 = 6*2
%e s(7)-s(3) = 21-3 = 18 = 6*3
%e s(9)-s(1) = 55-1 = 54 = 6*9
%e s(9)-s(6) = 55-13 = 42 = 6*7
%e s(10)-s(4) = 89-5 = 84 =6*14
%t s[n_] := s[n] = Fibonacci[n + 1]; z1 = 500; z2 = 60;
%t f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
%t Table[s[n], {n, 1, 30}]
%t u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t Table[u[m], {m, 1, z1}] (* A204922 *)
%t v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
%t c = 6; t = d[c] (* A205856 *)
%t k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
%t j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
%t Table[k[n], {n, 1, z2}] (* A205857 *)
%t Table[j[n], {n, 1, z2}] (* A205858 *)
%t Table[s[k[n]]-s[j[n]], {n, 1, z2}] (* A205859 *)
%t Table[(s[k[n]]-s[j[n]])/c, {n,1,z2}] (* A205860 *)
%Y Cf. A204892, A205857, A205859.
%K nonn
%O 1,2
%A _Clark Kimberling_, Feb 02 2012
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