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.

1, 2, 1, 4, 10, 11, 22, 11, 46, 45, 44, 75, 121, 111, 197, 122, 319, 244, 122, 510, 499, 488, 836, 832, 1352, 1342, 1231, 2189, 2185, 1353, 3542, 3538, 2706, 1353, 5731, 5656, 5534, 5412, 9273, 9272, 9271, 9227, 15004, 14994, 14883, 13652

Offset

1,2

Comments

For a guide to related sequences, see A205840.

Links

Table of n, a(n) for n=1..46.

Example

The first six terms match these differences:
s(5)-s(3) = 8-3 = 5 = 5*1
s(6)-s(3) = 13-3 = 10 = 5*2
s(6)-s(5) = 13-8 = 5 = 5*1
s(7)-s(1) = 21-1 = 20 = 5*4
s(9)-s(4) = 55-5 = 50 = 5*10
s(10)-s(8) = 89-34 = 55 =5*11

Mathematica

s[n_] := s[n] = Fibonacci[n + 1]; z1 = 500; z2 = 60;
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 = 5; t = d[c]    (* A205851 *)
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}]   (* A205852 *)
Table[j[n], {n, 1, z2}]   (* A205853 *)
Table[s[k[n]]-s[j[n]], {n, 1, z2}] (* A205854 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205855 *)

Crossrefs

Cf. A204892, A205852, A205854.

Sequence in context: A352093 A038195 A212770 * A329709 A038521 A134654

Adjacent sequences: A205852 A205853 A205854 * A205856 A205857 A205858

Keyword

nonn

Author

Clark Kimberling, Feb 02 2012

Status

approved