A234171 - OEIS

A234171

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

%I #6 Jun 19 2022 01:50:50

%S 4536,70486,1173940,20235390,354809676,6280203692,111690695276,

%T 1992506433044,35594422747852,636660168609324,11391644399534828,

%U 203967124960446932,3652089234220796108,65424063948417919724

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

%H R. H. Hardin, <a href="/A234171/b234171.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 33*a(n-1) +323*a(n-2) -20479*a(n-3) +66827*a(n-4) +4196961*a(n-5) -32408967*a(n-6) -381895309*a(n-7) +4395837462*a(n-8) +15113145790*a(n-9) -293548976068*a(n-10) -51289577932*a(n-11) +10922776315912*a(n-12) -16766805352904*a(n-13) -235952101172000*a(n-14) +626750889441184*a(n-15) +2967198544937088*a(n-16) -10881957631245888*a(n-17) -20625630149777664*a(n-18) +106077230575696640*a(n-19) +62012982701743616*a(n-20) -603993107147691008*a(n-21) +80220923857108992*a(n-22) +1983943732124129280*a(n-23) -1120944653090611200*a(n-24) -3571475321182953472*a(n-25) +3062535903549603840*a(n-26) +3148640202567516160*a(n-27) -3550878140723822592*a(n-28) -1004211355174305792*a(n-29) +1711073233311105024*a(n-30) -31999222443147264*a(n-31) -285978658647048192*a(n-32) +29150317966786560*a(n-33) +14870074192035840*a(n-34) -1882287872409600*a(n-35).

%e Some solutions for n=2:

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

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

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

%Y Column 2 of A234175.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 20 2013