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A235289 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant stress 1X1 tilings) 9

%I

%S 20,40,40,68,68,68,136,104,104,136,236,188,148,188,236,472,304,248,

%T 248,304,472,836,572,380,380,380,572,836,1672,968,680,544,544,680,968,

%U 1672,3020,1868,1108,908,740,908,1108,1868,3020,6040,3280,2072,1400,1168,1168

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant stress 1X1 tilings)

%C Table starts

%C ...20...40...68..136..236...472...836..1672..3020..6040.11108.22216.41516

%C ...40...68..104..188..304...572...968..1868..3280..6428.11624.22988.42544

%C ...68..104..148..248..380...680..1108..2072..3548..6824.12148.23768.43580

%C ..136..188..248..380..544...908..1400..2492..4096..7628.13208.25340.45664

%C ..236..304..380..544..740..1168..1724..2944..4676..8464.14300.26944.47780

%C ..472..572..680..908.1168..1724..2408..3884..5872.10172.16520.30188.52048

%C ..836..968.1108.1400.1724..2408..3220..4952..7196.12008.18868.33560.56444

%C .1672.1868.2072.2492.2944..3884..4952..7196..9952.15788.23672.40412.65344

%C .3020.3280.3548.4096.4676..5872..7196..9952.13220.20080.28988.47776.74756

%C .6040.6428.6824.7628.8464.10172.12008.15788.20080.28988.39944.62828.93904

%C Empirical: T(n,k)=Number of (n+1)X(k+1) 0..2+i arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 2+2*i (constant stress 1X1 tilings) for i=1..4(..?)

%H R. H. Hardin, <a href="/A235289/b235289.txt">Table of n, a(n) for n = 1..568</a>

%F Empirical for column k (the recurrence for k=2..7 also works for k=1; apparently every row and column satisfies the same order 6 recurrence):

%F diagonal: a(n) = a(n-1) +9*a(n-2) -9*a(n-3) -26*a(n-4) +26*a(n-5) +24*a(n-6) -24*a(n-7)

%F k=1: a(n) = 2*a(n-1) +3*a(n-2) -6*a(n-3)

%F k=2..7: a(n) = 3*a(n-1) +3*a(n-2) -15*a(n-3) +4*a(n-4) +18*a(n-5) -12*a(n-6)

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 05 2014

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Last modified January 19 12:40 EST 2022. Contains 350465 sequences. (Running on oeis4.)