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A205845 [s(k)-s(j)]/3, where the pairs (k,j) are given by A205842 and A205843, and s(k) denotes the (k+1)-st Fibonacci number. 5
1, 2, 1, 4, 6, 11, 7, 18, 14, 7, 29, 28, 27, 47, 41, 77, 76, 75, 48, 125, 124, 123, 96, 48, 203, 199, 192, 185, 328, 322, 281, 532, 528, 521, 514, 329, 861, 857, 850, 843, 658, 329, 1393, 1392, 1391, 1364, 1316, 1268, 2254, 2248, 2207, 1926, 3648 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For a guide to related sequences, see A205840.

The first six terms match these differences:

s(4)-s(2) = 5-2 = 3 = 3*1

s(5)-s(2) = 8-2 = 6 = 3*2

s(5)-s(4) = 8-5 = 3 = 3*1

s(6)-s(1) = 13-1 = 12 = 3*4

s(7)-s(3) = 21-3 = 18 = 3*6

s(8)-s(1) = 34-1 = 33 + 3*11

(See the program at A205842.)

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

The first six terms match these differences:

s(4)-s(2) = 5-2 = 3 = 3*1

s(5)-s(2) = 8-2 = 6 = 3*2

s(5)-s(4) = 8-5 = 3 = 3*1

s(6)-s(1) = 13-1 = 12 = 3*4

s(7)-s(3) = 21-3 = 18 = 3*6

s(8)-s(1) = 34-1 = 33 + 3*11

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 = 3; t = d[c]       (* A205841 *)

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}]      (* A205842 *)

Table[j[n], {n, 1, z2}]      (* A205843 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205844 *)

Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205845 *)

CROSSREFS

Cf. A204890, A205842, A205845.

Sequence in context: A283309 A054408 A285637 * A034424 A095012 A192781

Adjacent sequences:  A205842 A205843 A205844 * A205846 A205847 A205848

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 01 2012

STATUS

approved

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Last modified July 2 09:13 EDT 2020. Contains 335398 sequences. (Running on oeis4.)