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A189355 T(n,k) is the number of n X k array permutations with each element moving one space diagonally, horizontally or vertically.

%I A189355 #10 Aug 24 2024 15:45:52
%S A189355 0,1,1,0,4,0,1,13,13,1,0,45,48,45,0,1,160,557,557,160,1,0,565,3632,
%T A189355 12592,3632,565,0,1,2005,30769,237297,237297,30769,2005,1,0,7108,
%U A189355 229248,4791913,10252800,4791913,229248,7108,0,1,25209,1815601,94635005
%N A189355 T(n,k) is the number of n X k array permutations with each element moving one space diagonally, horizontally or vertically.
%C A189355 Table starts
%C A189355 .0.....1.........0............1................0....................1
%C A189355 .1.....4........13...........45..............160..................565
%C A189355 .0....13........48..........557.............3632................30769
%C A189355 .1....45.......557........12592...........237297..............4791913
%C A189355 .0...160......3632.......237297.........10252800............519621497
%C A189355 .1...565.....30769......4791913........519621497..........64731638400
%C A189355 .0..2005....229248.....94635005......24728774144........7675175968337
%C A189355 .1..7108...1815601...1883785285....1206541811872......927311536349401
%C A189355 .0.25209..13960720..37399042560...58289324009008...111267210412798665
%C A189355 .1.89401.108880333.743166198493.2827118724742121.13385995390731369181
%H A189355 R. H. Hardin, <a href="/A189355/b189355.txt">Table of n, a(n) for n = 1..144</a>
%e A189355 Some solutions for 5X3
%e A189355 ..1..0..5....4..5..1....4..0..5....4..5..1....3..5..1....1..2..5....3..2..5
%e A189355 ..6..3..2....7..0..2....6..1..2....0..8..2....0..8..2....0..7..8....0..1..4
%e A189355 ..7..8..4....3..6.11....3..8..7....3..6..7....9..4..7...10..3..4....9..8..7
%e A189355 .12.11.10...10.14..8...12.11.14...13.14.10...12..6.14...13..6.14...12..6.10
%e A189355 ..9.14.13....9.12.13...13..9.10....9.12.11...13.10.11....9.12.11...13.14.11
%Y A189355 Cf. A189186.
%K A189355 nonn,tabl
%O A189355 1,5
%A A189355 _R. H. Hardin_, Apr 20 2011