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A205860 [s(k)-s(j)]/6, where the pairs (k,j) are given by A205857 and A205858, and s(k) denotes the (k+1)-st Fibonacci number. 3
1, 2, 3, 9, 7, 14, 38, 24, 62, 48, 24, 96, 164, 161, 266, 264, 257, 425, 329, 696, 682, 658, 634, 1127, 1124, 963, 1824, 1823, 2951, 2937, 2913, 2889, 2255, 4776, 4774, 4767, 4510, 7704, 12504, 12502, 12495, 12238, 7728, 20232, 20230, 20223 (list; graph; refs; listen; history; text; internal format)
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(2) = 8-2 = 6 = 6*1

s(6)-s(1) = 13-1 = 12 = 6*2

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

s(9)-s(1) = 55-1 = 54 = 6*9

s(9)-s(6) = 55-13 = 42 = 6*7

s(10)-s(4) = 89-5 = 84 =6*14

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 = 6; t = d[c]    (* A205856 *)

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}]     (* A205857 *)

Table[j[n], {n, 1, z2}]     (* A205858 *)

Table[s[k[n]]-s[j[n]], {n, 1, z2}]    (* A205859 *)

Table[(s[k[n]]-s[j[n]])/c, {n, 1, z2}]  (* A205860 *)

CROSSREFS

Cf. A204892, A205857, A205859.

Sequence in context: A016634 A244257 A171054 * A318948 A328424 A299773

Adjacent sequences:  A205857 A205858 A205859 * A205861 A205862 A205863

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 02 2012

STATUS

approved

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Last modified August 11 06:25 EDT 2020. Contains 336422 sequences. (Running on oeis4.)