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A256659 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). 2

%I #5 Apr 09 2015 07:59:14

%S 4,7,6,12,11,10,20,19,18,16,25,32,31,29,26,33,40,52,50,47,42,38,53,65,

%T 84,81,76,68,41,61,86,105,136,131,123,110,46,66,99,139,170,220,212,

%U 199,178,54,74,107,160,225,275,356,343,322,288,59,87,120,173,259

%N 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 See A256655 for definitions. This array and the array at A256658 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 Northwest corner:

%e 4 7 12 20 25 33 38 41 46

%e 6 11 19 32 40 53 61 66 74

%e 10 18 31 52 65 86 99 102 120

%e 16 29 50 84 105 139 160 173 194

%e 26 47 81 136 170 225 259 280 314

%t b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];

%t h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];

%t g = h[18]; r[0] = {0};

%t r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];

%t t = Table[Last[r[n]], {n, 0, 1000}]; (* A256656 *)

%t TableForm[Table[Flatten[-1 + Position[t, b[n]]], {n, 2, 8}]] (* A256658 *)

%t TableForm[Table[Flatten[-1 + Position[t, -b[n]]], {n, 2, 8}]] (* A256659 *)

%Y Cf. A000045, A256655, A246658.

%K nonn,tabl,easy

%O 1,1

%A _Clark Kimberling_, Apr 08 2015

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)