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A187859 Number of 4-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions. 1

%I #10 Apr 26 2018 08:56:39

%S 0,0,216,968,2754,5428,9237,14040,19837,26628,34413,43192,52965,63732,

%T 75493,88248,101997,116740,132477,149208,166933,185652,205365,226072,

%U 247773,270468,294157,318840,344517,371188,398853,427512,457165,487812

%N Number of 4-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

%C Row 4 of A187857.

%H R. H. Hardin, <a href="/A187859/b187859.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 497*n^2 - 2652*n + 3448 for n>5.

%F Conjectures from _Colin Barker_, Apr 26 2018: (Start)

%F G.f.: x^3*(216 + 320*x + 498*x^2 - 146*x^3 + 247*x^4 - 141*x^5) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

%F (End)

%e Some solutions for 4 X 4:

%e ..0..0..0..0....3..2..4..0....0..0..0..0....0..4..0..0....0..0..0..4

%e ..0..0..0..0....0..1..0..0....0..4..3..0....0..0..3..0....0..3..2..0

%e ..4..3..2..0....0..0..0..0....2..1..0..0....1..0..2..0....0..0..0..1

%e ..0..0..1..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

%Y Cf. A187857.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 14 2011

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)