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.

1, 2, 5, 11, 23, 22, 61, 122, 61, 255, 244, 418, 416, 676, 671, 1771, 1769, 1353, 2828, 2767, 2706, 4636, 7502, 7497, 6826, 12139, 12138, 12116, 19641, 15005, 31781, 31779, 31363, 30010, 51414, 83143, 134618, 83204, 217822, 166408, 83204

Offset: 1

Author

Clark Kimberling, Feb 02 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A205840.

Examples

			The first three terms match these differences:
s(6)-s(3) = 13-3 = 10 = 10*1
s(7)-s(1) = 21-1 = 20 = 10*2
s(9)-s(4) = 55-5 = 50 = 10*5
		

Crossrefs

Cf. A204892, A205877, A205879.

Programs

Mathematica

s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]  (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 10; t = d[c]    (* A205876 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]   (* A205877 *)
Table[j[n], {n, 1, z2}]   (* A205878 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205879 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205880 *)