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

1,2

Comments

For a guide to related sequences, see A205840.

Links

Table of n, a(n) for n=1..41.

Example

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

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 *)

Crossrefs

Cf. A204892, A205877, A205879.

Sequence in context: A033120 A365243 A091617 * A009293 A180337 A257130

Adjacent sequences: A205877 A205878 A205879 * A205881 A205882 A205883

Keyword

nonn

Author

Clark Kimberling, Feb 02 2012

Status

approved