A329094 a(n) is the number of solutions when placing the numbers 1..n in an n X n square according to the rules in the Comments section.

1, 1, 1, 1, 1, 3, 3, 8, 17, 18, 51, 69, 126, 286, 485, 1180, 2245, 4312, 7247, 19559, 41403, 66454, 161131, 337495, 710899, 1286527, 3069554, 7100614, 15046664, 29090692, 57797782, 144576706, 313441617, 628544270, 1278592587, 3304149943, 7192582862

Offset

1,6

Comments

Place a 1 in the upper left corner of the square. Let k be the number placed last. At each step place k+1 at a distance k vertically or horizontally from k. Solutions are counted up to mirroring in the backward diagonal. That is, all solutions have 2 to the right of 1. Obviously, n is the largest possible value since the next step will inevitably lead outside the square.

Links

Table of n, a(n) for n=1..37.

Example

Sample solutions:
  n=6                  n=7                     n=8
  1  2  -  -  -  -     1  2  -  -  -  -  -     1  2  -  -  -  -  8  -
  -  -  -  -  -  -     7  5  -  -  -  -  6     -  -  -  -  -  -  -  -
  -  3  -  -  -  -     -  3  -  -  -  -  -     5  3  -  -  4  -  -  -
  -  -  -  -  -  -     -  -  -  -  -  -  -     -  -  -  -  -  -  -  -
  -  -  -  -  -  -     -  -  -  -  -  -  -     -  -  -  -  -  -  -  -
  6  4  -  -  -  5     -  4  -  -  -  -  -     -  -  -  -  -  -  -  -
                       -  -  -  -  -  -  -     -  -  -  -  -  -  -  -
                                               6  -  -  -  -  -  7  -

Crossrefs

Cf. A308353.

Sequence in context: A104864 A300367 A296106 * A327327 A370640 A328976

Adjacent sequences: A329091 A329092 A329093 * A329095 A329096 A329097

Keyword

nonn

Author

Lars Blomberg, Nov 04 2019

Status

approved