A234722 - OEIS

A234722

Number of (n+1) X (2+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).

%I #6 Jun 20 2022 19:00:15

%S 1096,3976,12464,48976,168928,692512,2531888,10649920,40456096,

%T 173104096,675830384,2926809856,11669180128,50984087392,206719128368,

%U 909199934080,3737628522016,16522547685856,68705695864304,304909972231936

%N Number of (n+1) X (2+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="/A234722/b234722.txt">Table of n, a(n) for n = 1..210</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=5:

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

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

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

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

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

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

%Y Column 2 of A234728.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 30 2013