A186862 Number of 3-step king's tours on an n X n board summed over all starting positions.

0, 24, 160, 408, 768, 1240, 1824, 2520, 3328, 4248, 5280, 6424, 7680, 9048, 10528, 12120, 13824, 15640, 17568, 19608, 21760, 24024, 26400, 28888, 31488, 34200, 37024, 39960, 43008, 46168, 49440, 52824, 56320, 59928, 63648, 67480, 71424, 75480, 79648, 83928, 88320, 92824

Offset

1,2

Links

J. Volkmar Schmidt, Table of n, a(n) for n = 1..50

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Formula

a(n) = 56*n^2 - 144*n + 88 = 8*(n-1)*(7*n-11).

G.f.: 8*x^2*(3+11*x)/(1-x)^3. - Colin Barker, Jan 22 2012

Example

Some solutions for 3 X 3:
  0 0 0    0 1 0    2 1 0    0 1 0    0 0 0    0 0 0    0 1 0    0 1 3
  3 0 0    2 3 0    3 0 0    0 2 3    0 1 0    0 0 0    2 0 0    0 2 0
  2 1 0    0 0 0    0 0 0    0 0 0    3 2 0    1 2 3    3 0 0    0 0 0

Crossrefs

Row 3 of A186861.

Sequence in context: A222002 A240268 A231341 * A305165 A294110 A136380

Adjacent sequences: A186859 A186860 A186861 * A186863 A186864 A186865

Keyword

nonn,easy

Author

R. H. Hardin, Feb 27 2011

Extensions

a(29)-a(42) from J. Volkmar Schmidt, Sep 03 2023

Status

approved