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Number of (n+1) X (2+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
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%I #6 Jun 20 2022 18:33:42

%S 272,980,3164,11984,40856,159004,551048,2185372,7639428,30731272,

%T 108061936,439375016,1551527016,6358076852,22519342100,92803479508,

%U 329391982880,1362841851812,4844325889344,20098730525504,71515038046716

%N Number of (n+1) X (2+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234884/b234884.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +46*a(n-2) -91*a(n-3) -852*a(n-4) +1670*a(n-5) +8364*a(n-6) -16318*a(n-7) -48531*a(n-8) +94856*a(n-9) +177211*a(n-10) -349287*a(n-11) -422181*a(n-12) +844527*a(n-13) +666796*a(n-14) -1362305*a(n-15) -697540*a(n-16) +1464198*a(n-17) +475379*a(n-18) -1029412*a(n-19) -204338*a(n-20) +455683*a(n-21) +52461*a(n-22) -118912*a(n-23) -7142*a(n-24) +16187*a(n-25) +376*a(n-26) -846*a(n-27).

%e Some solutions for n=4:

%e 1 0 3 5 4 5 2 1 2 0 3 2 5 2 5 2 5 4 0 3 2

%e 4 2 4 4 2 4 5 3 5 3 5 3 2 0 2 0 2 0 3 5 3

%e 1 0 1 3 0 1 2 1 2 2 3 0 4 1 4 1 4 1 2 3 2

%e 5 3 5 4 2 4 5 3 5 3 5 1 5 3 5 0 2 0 3 5 3

%e 3 2 3 1 0 1 1 0 3 2 3 0 3 0 1 3 4 1 2 3 0

%Y Column 2 of A234890.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 01 2014