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A234661 Number of (n+1) X (3+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant-stress 1 X 1 tilings). 1

%I #6 Jun 20 2022 18:22:43

%S 11112,52646,250792,1219652,5969944,29828832,150093796,770712800,

%T 3987209216,21036841216,111842789152,605833742520,3306209148612,

%U 18360060158328,102661189926976,583256023283512,3333695013231256

%N Number of (n+1) X (3+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234661/b234661.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 37*a(n-1) -377*a(n-2) -2618*a(n-3) +77447*a(n-4) -294799*a(n-5) -4757619*a(n-6) +45540630*a(n-7) +61891376*a(n-8) -2437351502*a(n-9) +6395028748*a(n-10) +63315544498*a(n-11) -379499690085*a(n-12) -574635388877*a(n-13) +9755368316951*a(n-14) -11625591036256*a(n-15) -133055653485659*a(n-16) +418266455931349*a(n-17) +823106610584361*a(n-18) -5467891684835430*a(n-19) +1031251784123218*a(n-20) +36193728208088096*a(n-21) -44705964178611952*a(n-22) -124471844677347304*a(n-23) +241456322415418264*a(n-24) +272081034415319536*a(n-25) -671531537886950352*a(n-26) -480780534963511680*a(n-27) +1128701330288740800*a(n-28) +770576980895712000*a(n-29) -1120320571251686400*a(n-30) -920761444521216000*a(n-31) +573508008695808000*a(n-32) +665567689121280000*a(n-33) -74650786306560000*a(n-34) -247547977113600000*a(n-35) -49525866547200000*a(n-36) +32441969664000000*a(n-37) +15456946176000000*a(n-38) +1881169920000000*a(n-39).

%e Some solutions for n=2:

%e 2 0 1 1 6 5 2 6 3 3 3 2 1 6 4 4 0 1 4 5

%e 1 3 0 4 1 4 5 5 2 6 2 5 3 4 6 2 4 1 0 5

%e 5 3 4 4 6 5 2 6 1 1 1 0 6 3 1 1 0 1 4 5

%Y Column 3 of A234665.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2013

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