cp's OEIS Frontend

A187303 Number of 8-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions.

%I A187303 #10 Apr 23 2018 14:27:04
%S A187303 0,0,72,2028,12778,37124,81362,145100,231552,338044,465734,613212,
%T A187303 780752,968044,1175118,1401948,1648534,1914876,2200974,2506828,
%U A187303 2832438,3177804,3542926,3927804,4332438,4756828,5200974,5664876,6148534,6651948,7175118
%N A187303 Number of 8-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions.
%C A187303 Row 8 of A187296.
%H A187303 R. H. Hardin, <a href="/A187303/b187303.txt">Table of n, a(n) for n = 1..50</a>
%F A187303 Empirical: a(n) = 9878*n^2 - 79388*n + 143388 for n>13.
%F A187303 Conjectures from _Colin Barker_, Apr 23 2018: (Start)
%F A187303 G.f.: 2*x^3*(36 + 906*x + 3455*x^2 + 2401*x^3 + 3148*x^4 - 196*x^5 + 1607*x^6 - 1337*x^7 + 579*x^8 - 705*x^9 + 137*x^10 - 155*x^11 + 15*x^12 - 13*x^13) / (1 - x)^3.
%F A187303 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>16.
%F A187303 (End)
%e A187303 Some solutions for 4 X 4:
%e A187303 ..0..1..0..0....1..6..5..0....0..6..5..7....6..0..7..0....8..7..6..2
%e A187303 ..0..6..5..7....0..0..4..0....0..0..4..0....5..1..0..0....0..0..5..1
%e A187303 ..3..2..4..0....2..7..3..8....2..1..3..8....4..0..8..0....0..0..4..3
%e A187303 ..0..0..0..8....0..0..0..0....0..0..0..0....3..2..0..0....0..0..0..0
%Y A187303 Cf. A187296.
%K A187303 nonn
%O A187303 1,3
%A A187303 _R. H. Hardin_, Mar 08 2011