A317612 For k >= 1, fill a k X k square with the numbers 1 to k^2 by rows left to right and top to bottom; then read the square by a square clockwise spiral beginning at the top left and spiraling inwards.

1, 1, 2, 4, 3, 1, 2, 3, 6, 9, 8, 7, 4, 5, 1, 2, 3, 4, 8, 12, 16, 15, 14, 13, 9, 5, 6, 7, 11, 10, 1, 2, 3, 4, 5, 10, 15, 20, 25, 24, 23, 22, 21, 16, 11, 6, 7, 8, 9, 14, 19, 18, 17, 12, 13, 1, 2, 3, 4, 5, 6, 12, 18, 24, 30, 36, 35, 34, 33, 32, 31, 25, 19, 13, 7, 8, 9, 10, 11, 17, 23, 29, 28, 27, 26, 20, 14, 15, 16, 22, 21, 1, 2, 3, 4, 5, 6, 7, 14, 21, 28, 35, 42, 49, 48, 47, 46, 45, 44, 43

Offset

1,3

Comments

Inspired by A317186.

The final term in the k X k spiral is A031878(k+1).

Links

Table of n, a(n) for n=1..110.

Example

  1 => 1;
.
  1---2
      |
  3---4  =>  1, 2, 4, 3;
.
  1---2---3
          |
  4---5   6
  |       |
  7---8---9  =>  1, 2, 3, 6, 9, 8, 7, 4, 5;
.
   1---2---3---4
               |
   5---6---7   8
   |       |   |
   9  10--11  12
   |           |
  13--14--15--16
.
  => 1, 2, 3, 4, 8, 12, 16, 15, 14, 13, 9, 5, 6, 7, 11, 10;
.
   1---2---3---4---5
                   |
   6---7---8---9  10
   |           |   |
  11  12--13  14  15
   |   |       |   |
  16  17--18--19  20
   |               |
  21--22--23--24--25
.
  => 1, 2, 3, 4, 5, 10, 15, 20, 25, 24, 23, 22, 21, 16, 11, 6, 7, 8, 9, 14, 19, 18, 17, 12, 13;
.
   1---2---3---4---5---6
                       |
   7---8---9--10--11  12
   |               |   |
  13  14--15--16  17  18
   |   |       |   |   |
  19  20  21--22  23  24
   |   |           |   |
  25  26--27--28--29  30
   |                   |
  31--32--33--34--35--36
.
  => 1, 2, 3, 4, 5, 6, 12, 18, 24, 30, 36, 35, 34, 33, 32, 31, 25, 19, 13, 7, 8, 9, 10, 11, 17, 23, 29, 28, 27, 26, 20, 14, 15, 16, 22, 21;

Mathematica

(* To form an n X n square table which begins left to right, then top to bottom *) a[i_, j_, n_] := j + n*(i - 1); f[n_] := Table[ a[i, j, n], {i, n}, {j, n}]

Crossrefs

Cf. A031878, A317186.

Sequence in context: A227862 A229802 A106581 * A070402 A125941 A347270

Adjacent sequences: A317609 A317610 A317611 * A317613 A317614 A317615

Keyword

easy,nonn

Author

George E. Laham II and Robert G. Wilson v, Aug 01 2018

Status

approved