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

Author

R. H. Hardin, Feb 27 2011

Keywords

• nonn
• easy

Examples

			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
		

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).

Crossrefs

Row 3 of A186861.

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

Extensions

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