A186855 Number of 6-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

16, 800, 8352, 34448, 91328, 186544, 322528, 498320, 712080, 963008, 1251104, 1576368, 1938800, 2338400, 2775168, 3249104, 3760208, 4308480, 4893920, 5516528, 6176304, 6873248, 7607360, 8378640, 9187088, 10032704, 10915488, 11835440, 12792560, 13786848

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

a(n) = 18584*n^2 - 102168*n + 126288 for n > 7.

Example

Some solutions for 5 X 5:
  0 0 0 0 6     1 0 0 0 0     0 4 0 0 0     0 0 0 0 0
  0 0 5 2 0     0 0 2 0 6     0 0 0 0 6     0 0 0 3 6
  0 3 0 0 0     3 0 0 0 0     3 0 5 0 1     0 4 1 0 0
  0 0 0 4 1     0 0 0 5 0     0 0 2 0 0     0 0 0 5 2
  0 0 0 0 0     0 4 0 0 0     0 0 0 0 0     0 0 0 0 0

Prog

(PARI) row(6, 30) \\ row(m, n) defined in A186851. - Andrew Howroyd, Jan 02 2023

Crossrefs

Row 6 of A186851.

Sequence in context: A231083 A173984 A364510 * A159872 A220750 A166187

Adjacent sequences: A186852 A186853 A186854 * A186856 A186857 A186858

Keyword

nonn

Author

R. H. Hardin, Feb 27 2011

Extensions

Terms a(16) and beyond from Andrew Howroyd, Jan 02 2023

Status

approved