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A205875 [s(k)-s(j)]/9, where the pairs (k,j) are given by A205872 and A205873, and s(k) denotes the (k+1)-st Fibonacci number. 3
2, 6, 9, 25, 16, 41, 32, 16, 64, 176, 287, 281, 464, 642, 1216, 1967, 1958, 1942, 1926, 3184, 3178, 2897, 5136, 8336, 8330, 8049, 5152, 13488, 13482, 13201, 10304, 5152, 21824, 20608, 35312, 35310, 57136, 56672, 92448, 92439, 92423, 92407 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For a guide to related sequences, see A205840.

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

The first six terms match these differences:

s(7)-s(3) = 21-3 = 18 = 9*2

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

s(10)-s(5) = 89-8 = 81 = 9*9

s(12)-s(5) = 233-8 = 225 = 9*25

s(12)-s(10) = 233-89 = 144 = 9*16

s(13)-s(5) = 377-8 = 369 =9*41

MATHEMATICA

s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;

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 = 9; t = d[c]     (* A205871 *)

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}]       (* A205872 *)

Table[j[n], {n, 1, z2}]         (* A205873 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}]   (* A205874 *)

Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205875 *)

CROSSREFS

Cf. A204892, A205872, A205874.

Sequence in context: A077237 A056879 A006746 * A243558 A244427 A121624

Adjacent sequences:  A205872 A205873 A205874 * A205876 A205877 A205878

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 02 2012

STATUS

approved

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Last modified May 16 12:19 EDT 2021. Contains 343942 sequences. (Running on oeis4.)