A205860 - OEIS

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.

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

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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