A083047 - OEIS

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

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OFFSET

0,2

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

LINKS

Table of n, a(n) for n=0..66.

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 ...