A183805 - OEIS

A183805

1/16 the number of (n+1) X 4 binary arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

%I #12 Apr 05 2018 03:05:13

%S 9,55,322,1953,11619,70044,418925,2518389,15091626,90619253,543451183,

%T 3261698460,19566441353,117412757177,704423288546,4226740369841,

%U 25359685459275,152160965127516,912955035168789,5477770757446957

%N 1/16 the number of (n+1) X 4 binary arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

%C Column 3 of A183811.

%H R. H. Hardin, <a href="/A183805/b183805.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 6*a(n-1) + 12*a(n-2) - 83*a(n-3) + 56*a(n-4) + 60*a(n-5).

%F Empirical g.f.: x*(9 + x - 116*x^2 + 108*x^3 + 98*x^4) / ((1 - 2*x)*(1 - 6*x)*(1 + 2*x - 8*x^2 - 5*x^3)). - _Colin Barker_, Apr 04 2018

%e Some solutions with upper left block zero for 3 X 4:

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

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

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

%Y Cf. A183811.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 07 2011