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