login
Number of (n+1) X (4+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 7 (constant-stress 1 X 1 tilings).
1

%I #6 Jun 20 2022 18:58:09

%S 19120,48976,116168,357208,1000264,3403528,10632200,38594056,

%T 129877960,493469896,1750807688,6882950728,25404230344,102540693448,

%U 390317557640,1608662074696,6277331314120,26307807293896,104776708099208

%N Number of (n+1) X (4+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 7 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234724/b234724.txt">Table of n, a(n) for n = 1..135</a>

%F Empirical: a(n) = 4*a(n-1) +137*a(n-2) -560*a(n-3) -8456*a(n-4) +35504*a(n-5) +310702*a(n-6) -1349320*a(n-7) -7561533*a(n-8) +34294092*a(n-9) +128206281*a(n-10) -615707400*a(n-11) -1548288698*a(n-12) +8040276992*a(n-13) +13333179376*a(n-14) -77453548480*a(n-15) -79946374816*a(n-16) +552146144704*a(n-17) +309222145232*a(n-18) -2893327015040*a(n-19) -567224779296*a(n-20) +10948880162304*a(n-21) -974085452928*a(n-22) -28950298675200*a(n-23) +9103597862400*a(n-24) +50436504576000*a(n-25) -24908850432000*a(n-26) -51674112000000*a(n-27) +32903055360000*a(n-28) +23410114560000*a(n-29) -17557585920000*a(n-30).

%e Some solutions for n=3:

%e 1 5 1 6 1 6 6 6 6 5 4 0 5 1 5 7 1 4 1 6

%e 4 1 4 2 4 7 0 7 0 6 0 3 1 4 1 4 5 1 5 3

%e 1 5 1 6 1 1 1 1 1 0 6 2 7 3 7 6 0 3 0 5

%e 3 0 3 1 3 7 0 7 0 6 3 6 4 7 4 3 4 0 4 2

%Y Column 4 of A234728.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 30 2013