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Number of (n+1) X 4 binary arrays with each element of every 2 X 2 subblock being the sum mod 2 of two others.
1

%I #8 Apr 05 2018 09:08:17

%S 88,542,3357,21068,132152,831331,5226955,32887826,206882773,

%T 1301662324,8189126429,51523012575,324155480581,2039448592803,

%U 12831234573276,80728397862748,507905656032918,3195511917733141,20104693948800956

%N Number of (n+1) X 4 binary arrays with each element of every 2 X 2 subblock being the sum mod 2 of two others.

%C Column 3 of A183845.

%H R. H. Hardin, <a href="/A183839/b183839.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 8*a(n-1) + 3*a(n-2) - 117*a(n-3) + 165*a(n-4) + 255*a(n-5) - 553*a(n-6) + 34*a(n-7) + 308*a(n-8) - 96*a(n-9).

%F Empirical g.f.: x*(88 - 162*x - 1243*x^2 + 2882*x^3 + 2431*x^4 - 8190*x^5 + 1356*x^6 + 4456*x^7 - 1504*x^8) / (1 - 8*x - 3*x^2 + 117*x^3 - 165*x^4 - 255*x^5 + 553*x^6 - 34*x^7 - 308*x^8 + 96*x^9). - _Colin Barker_, Apr 05 2018

%e Some solutions for 3 X 4:

%e ..1..1..0..1....1..1..0..1....0..1..0..1....0..1..0..0....1..0..1..1

%e ..0..1..0..1....1..0..1..1....1..1..1..0....1..1..1..1....1..0..1..0

%e ..0..1..1..1....1..1..0..1....0..1..0..1....0..0..0..0....1..0..1..0

%Y Cf. A183845.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 07 2011