cp's OEIS Frontend

A187857 T(n,k)=Number of n-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on a kXk board summed over all starting positions.

%I A187857 #8 Jul 22 2025 10:55:32
%S A187857 1,4,0,9,5,0,16,27,2,0,25,65,81,0,0,36,119,254,216,0,0,49,189,578,968,
%T A187857 486,0,0,64,275,1030,2754,3320,846,0,0,81,377,1610,5428,11986,9932,
%U A187857 1206,0,0,100,495,2318,9237,26836,47962,26584,1008,0,0,121,629,3154,14040
%N A187857 T(n,k)=Number of n-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on a kXk board summed over all starting positions.
%C A187857 Table starts
%C A187857 .1.4....9.....16......25.......36........49.......64.......81.....100.....121
%C A187857 .0.5...27.....65.....119......189.......275......377......495.....629.....779
%C A187857 .0.2...81....254.....578.....1030......1610.....2318.....3154....4118....5210
%C A187857 .0.0..216....968....2754.....5428......9237....14040....19837...26628...34413
%C A187857 .0.0..486...3320...11986....26836.....50378....81124...120051..166504..220483
%C A187857 .0.0..846...9932...47962...126397....262409...452766...707541.1017934.1387600
%C A187857 .0.0.1206..26584..180750...568870...1314428..2456614..4062007.6094090
%C A187857 .0.0.1008..61668..636102..2432312...6343874.12918800.22675997
%C A187857 .0.0..414.124880.2090520..9934272..29607932.65963326
%C A187857 .0.0....0.219008.6387404.38766870.133665550
%H A187857 R. H. Hardin, <a href="/A187857/b187857.txt">Table of n, a(n) for n = 1..130</a>
%F A187857 Empirical: T(1,k) = k^2
%F A187857 Empirical: T(2,k) = 8*k^2 - 18*k + 9 for k>1
%F A187857 Empirical: T(3,k) = 64*k^2 - 252*k + 238 for k>3
%F A187857 Empirical: T(4,k) = 497*k^2 - 2652*k + 3448 for k>5
%F A187857 Empirical: T(5,k) = 3763*k^2 - 25044*k + 40644 for k>7
%F A187857 Empirical: T(6,k) = 28294*k^2 - 224508*k + 433614 for k>9
%F A187857 Empirical: T(7,k) = 211612*k^2 - 1941340*k + 4328678 for k>11
%F A187857 Empirical: T(8,k) = 1575830*k^2 - 16367550*k + 41250447 for k>13
%F A187857 Empirical: T(9,k) = 11710007*k^2 - 135575032*k + 380311550 for k>15
%F A187857 Empirical: T(10,k) = 86897560*k^2 - 1108193530*k + 3420011978 for k>17
%e A187857 Some n=4 solutions for 4X4
%e A187857 ..0..0..1..0....4..0..0..0....0..0..0..0....0..3..0..4....0..0..0..0
%e A187857 ..0..3..0..0....0..3..0..0....0..2..1..0....0..0..2..1....3..2..0..0
%e A187857 ..0..0..2..0....0..0..2..0....0..4..0..0....0..0..0..0....0..1..0..0
%e A187857 ..0..0..0..4....0..0..0..1....0..3..0..0....0..0..0..0....0..0..4..0
%Y A187857 Row 2 is A181890(n-2)
%K A187857 nonn,tabl
%O A187857 1,2
%A A187857 _R. H. Hardin_ Mar 14 2011