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A083047
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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)=ceil(x*T(n,k)), where x=(sqrt(5)+1)/2, n>=0, k>=0.
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16
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| First row is A000071 offset by 2, first column is A026352, main diagonal is A083048, anti-diagonal 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]
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EXAMPLE
| 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 ...
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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]]
(* From Jean-François Alcover, Jul 13 2011 *)
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CROSSREFS
| Cf. A026352, A083048, A083049, A083044, A083050.
Cf. A167198. [From Clark Kimberling, Oct 30 2009]
Sequence in context: A082463 A194962 A072793 * A191737 A161659 A089657
Adjacent sequences: A083044 A083045 A083046 * A083048 A083049 A083050
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 18 2003
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