login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 16
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; text; internal format)
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 ...

  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 ...

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-Fran├žois Alcover, Jul 13 2011 *)

CROSSREFS

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

Cf. A167198. - Clark Kimberling, Oct 30 2009

Sequence in context: A082463 A194962 A072793 * A191737 A161659 A089657

Adjacent sequences:  A083044 A083045 A083046 * A083048 A083049 A083050

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Apr 18 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 19 07:39 EST 2018. Contains 299330 sequences. (Running on oeis4.)