A205850 [s(k)-s(j)]/4, where the pairs (k,j) are given by A205847 and A205848, and s(k) denotes the (k+1)-st Fibonacci number.

1, 3, 2, 5, 4, 2, 8, 13, 22, 21, 19, 17, 34, 58, 57, 55, 53, 36, 94, 93, 91, 89, 72, 36, 152, 144, 246, 233, 399, 398, 396, 394, 377, 341, 305, 644, 610, 1045, 1044, 1042, 1040, 1023, 987, 951, 646, 1691, 1690, 1688, 1686, 1669, 1633, 1597, 1292, 646

Offset

1,2

Comments

For a guide to related sequences, see A205840.

Links

Table of n, a(n) for n=1..54.

Example

The first six terms match these differences:
s(4)-s(1) = 5-1 = 4 = 4*1
s(6)-s(1) = 13-1 = 12= 4*3
s(6)-s(4) = 13-5 = 8 = 4*2
s(7)-s(1) = 21-1 = 20 = 4*5
s(7)-s(4) = 21-5 = 16 = 4*4
s(7)-s(6) = 21-13 = 8 = 4*2

Mathematica

s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; 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 = 4; t = d[c]    (* A205846 *)
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}]    (* A205847 *)
Table[j[n], {n, 1, z2}]    (* A205848 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}](* A205849 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  A205850 *)

Crossrefs

Cf. A204892, A205845, A205849.

Sequence in context: A110661 A143124 A205400 * A204890 A307775 A239680

Adjacent sequences: A205847 A205848 A205849 * A205851 A205852 A205853

Keyword

nonn

Author

Clark Kimberling, Feb 02 2012

Status

approved