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A187607 Number of 3-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 11:39:10

%S 0,0,9,36,100,196,324,484,676,900,1156,1444,1764,2116,2500,2916,3364,

%T 3844,4356,4900,5476,6084,6724,7396,8100,8836,9604,10404,11236,12100,

%U 12996,13924,14884,15876,16900,17956,19044,20164,21316,22500,23716,24964

%N Number of 3-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 3 of A187606.

%H R. H. Hardin, <a href="/A187607/b187607.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 16*n^2 - 80*n + 100 for n>3.

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

%F G.f.: x^3*(9 + 9*x + 19*x^2 - 5*x^3) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

%F (End)

%e Some solutions for 5 X 5:

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

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

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

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

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

%Y Cf. A187606.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 11 2011

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Last modified July 23 11:07 EDT 2024. Contains 374549 sequences. (Running on oeis4.)