A083047 Square table read by antidiagonals forms a permutation of the natural numbers: T(n,0) = floor(n*x/(x-1))+1, T(n,k+1) = ceiling(x*T(n,k)), where x = (sqrt(5)+1)/2, n>=0, k>=0.

1, 2, 3, 4, 5, 6, 7, 9, 10, 8, 12, 15, 17, 13, 11, 20, 25, 28, 22, 18, 14, 33, 41, 46, 36, 30, 23, 16, 54, 67, 75, 59, 49, 38, 26, 19, 88, 109, 122, 96, 80, 62, 43, 31, 21, 143, 177, 198, 156, 130, 101, 70, 51, 34, 24, 232, 287, 321, 253, 211, 164, 114, 83, 56, 39, 27, 376

Offset: 0

Author

Paul D. Hanna, Apr 18 2003

Keywords

• nonn
• tabl

Comments

First row is A000071 offset by 2, first column is A026352, main diagonal is A083048, antidiagonal sums give A083049.

A083047 is an interspersion (hence a dispersion), with fractal sequence A167198. See A167198 for a construction of A083047 that does not refer to (1+sqrt(5))/2. - Clark Kimberling, Oct 30 2009

Examples

			Table begins:
   1  2  4   7  12  20  33  54   88  143  232  376 ...
   3  5  9  15  25  41  67 109  177  287  465  753 ...
   6 10 17  28  46  75 122 198  321  520  842 1363 ...
   8 13 22  36  59  96 156 253  410  664 1075 1740 ...
  11 18 30  49  80 130 211 342  554  897 1452 2350 ...
  14 23 38  62 101 164 266 431  698 1130 1829 2960 ...
  16 26 43  70 114 185 300 486  787 1274 2062 3337 ...
  19 31 51  83 135 219 355 575  931 1507 2439 3947 ...
  21 34 56  91 148 240 389 630 1020 1651 2672 4324 ...
  24 39 64 104 169 274 444 719 1164 1884 3049 4934 ...
  27 44 72 117 190 308 499 808 1308 2117 3426 5544 ...
		

Crossrefs

Cf. A026352, A083048, A083049, A083044, A083050.

Cf. A167198. - Clark Kimberling, Oct 30 2009

Programs

Mathematica

t[n_, 0] = Floor[n*GoldenRatio/(GoldenRatio - 1) + 1];
t[n_, k_] := t[n, k] = Ceiling[GoldenRatio*t[n, k-1]];
Flatten[Table[t[k-1, n-k ], {n, 12}, {k, n}] ][[;; 67]]
(* Jean-François Alcover, Jul 13 2011 *)