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T(n,k) = Number of (n+1)X(k+1) 0..2 arrays with 2X2 subblock determinants differing from horizontal neighbors and permanents differing from vertical neighbors.
14

%I #8 Dec 05 2019 08:21:04

%S 81,554,476,4020,6020,2766,28522,79644,61588,15728,203346,1042382,

%T 1476942,611694,89630,1448300,13544456,34564494,26010268,6120848,

%U 511044,10317234,176994692,804426380,1076391970,464115072,61390466,2913944

%N T(n,k) = Number of (n+1)X(k+1) 0..2 arrays with 2X2 subblock determinants differing from horizontal neighbors and permanents differing from vertical neighbors.

%C Table starts

%C .......81........554..........4020............28522.............203346

%C ......476.......6020.........79644..........1042382...........13544456

%C .....2766......61588.......1476942.........34564494..........804426380

%C ....15728.....611694......26010268.......1076391970........43934005004

%C ....89630....6120848.....464115072......34054078628......2458450081192

%C ...511044...61390466....8325468740....1085248304854....138728411577118

%C ..2913944..614898304..148827007430...34411101807016...7771632134436102

%C .16611380.6157484270.2659178147340.1090399519549578.435193195671122398

%H R. H. Hardin, <a href="/A205894/b205894.txt">Table of n, a(n) for n = 1..78</a>

%e Some solutions for n=3 k=3

%e ..0..0..1..1....2..1..0..0....1..1..2..1....0..0..1..1....0..0..2..0

%e ..2..2..1..2....0..2..1..2....1..0..1..2....1..1..2..0....0..2..2..2

%e ..1..1..0..2....1..2..1..0....0..2..1..2....1..2..2..2....1..1..2..2

%e ..1..2..2..2....1..2..2..1....0..2..2..2....1..2..0..0....2..1..2..0

%Y Column 1 is A205286.

%Y Row 1 is A186528.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 01 2012