cp's OEIS Frontend

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.

%I A205845 #8 Mar 30 2012 18:58:12
%S A205845 1,2,1,4,6,11,7,18,14,7,29,28,27,47,41,77,76,75,48,125,124,123,96,48,
%T A205845 203,199,192,185,328,322,281,532,528,521,514,329,861,857,850,843,658,
%U A205845 329,1393,1392,1391,1364,1316,1268,2254,2248,2207,1926,3648
%N 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.
%C A205845 For a guide to related sequences, see A205840.
%C A205845 The first six terms match these differences:
%C A205845 s(4)-s(2) = 5-2 = 3 = 3*1
%C A205845 s(5)-s(2) = 8-2 = 6 = 3*2
%C A205845 s(5)-s(4) = 8-5 = 3 = 3*1
%C A205845 s(6)-s(1) = 13-1 = 12 = 3*4
%C A205845 s(7)-s(3) = 21-3 = 18 = 3*6
%C A205845 s(8)-s(1) = 34-1 = 33 + 3*11
%C A205845 (See the program at A205842.)
%e A205845 The first six terms match these differences:
%e A205845 s(4)-s(2) = 5-2 = 3 = 3*1
%e A205845 s(5)-s(2) = 8-2 = 6 = 3*2
%e A205845 s(5)-s(4) = 8-5 = 3 = 3*1
%e A205845 s(6)-s(1) = 13-1 = 12 = 3*4
%e A205845 s(7)-s(3) = 21-3 = 18 = 3*6
%e A205845 s(8)-s(1) = 34-1 = 33 + 3*11
%t A205845 s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; z2 = 60;
%t A205845 f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
%t A205845 Table[s[n], {n, 1, 30}]
%t A205845 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A205845 Table[u[m], {m, 1, z1}]   (* A204922 *)
%t A205845 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A205845 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A205845 d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
%t A205845 c = 3; t = d[c]       (* A205841 *)
%t A205845 k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
%t A205845 j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
%t A205845 Table[k[n], {n, 1, z2}]      (* A205842 *)
%t A205845 Table[j[n], {n, 1, z2}]      (* A205843 *)
%t A205845 Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205844 *)
%t A205845 Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205845 *)
%Y A205845 Cf. A204890, A205842, A205845.
%K A205845 nonn
%O A205845 1,2
%A A205845 _Clark Kimberling_, Feb 01 2012