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A186862
Number of 3-step king's tours on an n X n board summed over all starting positions.
3
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
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
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Feb 27 2011
EXTENSIONS
a(29)-a(42) from J. Volkmar Schmidt, Sep 03 2023
STATUS
approved