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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 03:18 EST 2021. Contains 349625 sequences. (Running on oeis4.)