A187612 - OEIS

A187612

Number of 8-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.

%I #10 Apr 25 2018 10:12:29

%S 0,0,0,0,0,474,3780,12946,32869,68308,117760,187311,275272,379035,

%T 500919,639115,793623,964443,1151575,1355019,1574775,1810843,2063223,

%U 2331915,2616919,2918235,3235863,3569803,3920055,4286619,4669495,5068683,5484183

%N Number of 8-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 8 of A187606.

%H R. H. Hardin, <a href="/A187612/b187612.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 8156*n^2 - 114640*n + 385419 for n>13.

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

%F G.f.: x^6*(474 + 2358*x + 3028*x^2 + 4897*x^3 + 4759*x^4 - 1503*x^5 + 6086*x^6 - 1689*x^7 - 2608*x^8 + 2319*x^9 - 1809*x^10) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>16.

%F (End)

%Y Cf. A187606.

%K nonn

%O 1,6

%A _R. H. Hardin_, Mar 11 2011