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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.

%I A083047 #16 Dec 01 2016 01:35:37
%S A083047 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,
%T A083047 23,16,54,67,75,59,49,38,26,19,88,109,122,96,80,62,43,31,21,143,177,
%U A083047 198,156,130,101,70,51,34,24,232,287,321,253,211,164,114,83,56,39,27,376
%N 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.
%C A083047 First row is A000071 offset by 2, first column is A026352, main diagonal is A083048, antidiagonal sums give A083049.
%C A083047 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
%e A083047 Table begins:
%e A083047    1  2  4   7  12  20  33  54   88  143  232  376 ...
%e A083047    3  5  9  15  25  41  67 109  177  287  465  753 ...
%e A083047    6 10 17  28  46  75 122 198  321  520  842 1363 ...
%e A083047    8 13 22  36  59  96 156 253  410  664 1075 1740 ...
%e A083047   11 18 30  49  80 130 211 342  554  897 1452 2350 ...
%e A083047   14 23 38  62 101 164 266 431  698 1130 1829 2960 ...
%e A083047   16 26 43  70 114 185 300 486  787 1274 2062 3337 ...
%e A083047   19 31 51  83 135 219 355 575  931 1507 2439 3947 ...
%e A083047   21 34 56  91 148 240 389 630 1020 1651 2672 4324 ...
%e A083047   24 39 64 104 169 274 444 719 1164 1884 3049 4934 ...
%e A083047   27 44 72 117 190 308 499 808 1308 2117 3426 5544 ...
%t A083047 t[n_, 0] = Floor[n*GoldenRatio/(GoldenRatio - 1) + 1];
%t A083047 t[n_, k_] := t[n, k] = Ceiling[GoldenRatio*t[n, k-1]];
%t A083047 Flatten[Table[t[k-1, n-k ], {n, 12}, {k, n}] ][[;; 67]]
%t A083047 (* _Jean-François Alcover_, Jul 13 2011 *)
%Y A083047 Cf. A026352, A083048, A083049, A083044, A083050.
%Y A083047 Cf. A167198. - _Clark Kimberling_, Oct 30 2009
%K A083047 nonn,tabl
%O A083047 0,2
%A A083047 _Paul D. Hanna_, Apr 18 2003