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 A187608 Number of 4-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-bishop's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions. 1

%I #11 Apr 25 2018 11:48:52

%S 0,0,0,28,144,340,675,1120,1675,2340,3115,4000,4995,6100,7315,8640,

%T 10075,11620,13275,15040,16915,18900,20995,23200,25515,27940,30475,

%U 33120,35875,38740,41715,44800,47995,51300,54715,58240,61875,65620,69475,73440,77515

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

%C Row 4 of A187606.

%H R. H. Hardin, <a href="/A187608/b187608.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 55*n^2 - 380*n + 640 for n>5.

%F Conjectures from _Colin Barker_, Apr 25 2018: (Start)

%F G.f.: x^4*(28 + 60*x - 8*x^2 + 59*x^3 - 29*x^4) / (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 5 X 5:

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

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

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

%e ..1..0..0..4..0....0..0..0..4..0....0..0..0..0..1....0..0..0..0..0

%e ..0..0..0..0..3....0..0..0..0..3....0..0..0..0..0....0..0..0..0..0

%Y Cf. A187606.

%K nonn

%O 1,4

%A _R. H. Hardin_, Mar 11 2011

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Last modified August 9 08:03 EDT 2024. Contains 375034 sequences. (Running on oeis4.)