A216191 Triangle T read by rows: T(n,k) equals the Manhattan distance between n and k when integers are arranged in a spiral.

0, 1, 0, 2, 1, 0, 1, 2, 1, 0, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 2, 3, 2, 1, 0, 2, 1, 2, 3, 4, 3, 2, 1, 0, 3, 2, 3, 4, 5, 4, 3, 2, 1, 0, 2, 1, 2, 3, 4, 3, 4, 3, 2, 1, 0, 3, 2, 1, 2, 3

Offset

0,4

Comments

Spiral begins (0 at the center):

.

42--43--44--45--46--47--48

|

41 20--21--22--23--24--25

| | |

40 19 6---7---8---9 26

| | | | |

39 18 5 0---1 10 27

| | | | | |

38 17 4---3---2 11 28

| | | |

37 16--15--14--13--12 29

| |

36--35--34--33--32--31--30

Links

Table of n, a(n) for n=0..70.

Formula

T(n,n) = 0, T(n+1,n) = 1, T(n+2,n) = 2, T(n,k) <= n-k.

Example

Triangle begins, 0 <= k <= n:
  0
  1, 0
  2, 1, 0
  1, 2, 1, 0
  2, 3, 2, 1, 0
  1, 2, 3, 2, 1, 0
  2, 3, 4, 3, 2, 1, 0
  1, 2, 3, 2, 3, 2, 1, 0
  2, 1, 2, 3, 4, 3, 2, 1, 0
  3, 2, 3, 4, 5, 4, 3, 2, 1, 0
  2, 1, 2, 3, 4, 3, 4, 3, 2, 1, 0
  3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0
  4, 3, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0
  3, 2, 1, 2, 3, 4, 5, 4, 3, 4, 3, 2, 1, 0
  2, 3, 2, 1, 2, 3, 4, 3, 4, 5, 4, 3, 2, 1, 0
  3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0

Crossrefs

Sequence in context: A106262 A025870 A104276 * A268834 A285914 A096875

Adjacent sequences: A216188 A216189 A216190 * A216192 A216193 A216194

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 11 2013

Status

approved