cp's OEIS Frontend

A256658 Rectangular array by antidiagonals: row n consists of numbers k such that F(n+1) is the trace of the minimal alternating Fibonacci representation of k, where F = A000045 (Fibonacci numbers).

%I A256658 #4 Apr 09 2015 07:59:06
%S A256658 1,9,2,14,15,3,17,23,24,5,22,28,37,39,8,27,36,45,60,63,13,30,44,58,73,
%T A256658 97,102,21,35,49,71,94,118,157,165,34,43,57,79,115,152,191,254,267,55,
%U A256658 48,70,92,128,186,246,309,411,432,89,51,78,113,149,207,301
%N A256658 Rectangular array by antidiagonals:  row n consists of numbers k such that F(n+1) is the trace of the minimal alternating Fibonacci representation of k, where F = A000045 (Fibonacci numbers).
%C A256658 See A256655 for definitions.  This array and the array at A256659 partition the positive integers.  The row differences are Fibonacci numbers.  The columns satisfy the Fibonacci recurrence x(n) = x(n-1) + x(n-2).
%e A256658 Northwest corner:
%e A256658 1    9     14    17    22    27    30    35    43
%e A256658 2    15    23    28    36    44    49    57    70
%e A256658 3    24    37    45    58    71    79    92    113
%e A256658 5    39    69    73    94    115   128   149   183
%e A256658 8    63    97    118   152   186   207   241   296
%e A256658 13   102   157   191   246   301   335   390   479
%t A256658 b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];
%t A256658 h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];
%t A256658 g = h[18];  r[0] = {0};
%t A256658  r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
%t A256658 t = Table[Last[r[n]], {n, 0, 1000}];  (* A256656 *)
%t A256658 TableForm[Table[Flatten[-1 + Position[t, b[n]]], {n, 2, 8}]]   (* A256658 *)
%t A256658 TableForm[Table[Flatten[-1 + Position[t, -b[n]]], {n, 2, 8}]]  (* A256659 *)
%Y A256658 Cf. A000045, A256655, A256659.
%K A256658 nonn,tabl,easy
%O A256658 1,2
%A A256658 _Clark Kimberling_, Apr 08 2015