A187610 - OEIS

%I #11 Apr 25 2018 11:48:59

%S 0,0,0,0,96,711,2083,4758,8979,14434,21526,29978,39790,50962,63494,

%T 77386,92638,109250,127222,146554,167246,189298,212710,237482,263614,

%U 291106,319958,350170,381742,414674,448966,484618,521630,560002,599734,640826

%N Number of 6-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 6 of A187606.

%H R. H. Hardin, <a href="/A187610/b187610.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 680*n^2 - 7188*n + 18314 for n>9.

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

%F G.f.: x^5*(96 + 423*x + 238*x^2 + 546*x^3 + 243*x^4 - 312*x^5 + 403*x^6 - 277*x^7) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.

%F (End)

%e Some solutions for 5 X 5:

%e ..0..0..0..0..1....0..0..0..0..0....0..6..0..0..0....0..0..5..0..0

%e ..0..0..6..0..0....0..0..6..0..0....0..0..5..0..0....4..0..0..1..0

%e ..5..0..0..2..0....2..0..0..5..0....1..0..0..4..0....0..3..0..0..6

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

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

%Y Cf. A187606.

%K nonn

%O 1,5

%A _R. H. Hardin_, Mar 11 2011