A183776 - OEIS

%I #14 Jan 09 2025 15:44:09

%S 8,33,161,730,3435,15887,74148,344483,1604473,7462786,34738575,

%T 161631659,752241404,3500410439,16290047469,75805472562,352771994195,

%U 1641641366551,7639557462868,35551227927131,165441007206577,769893052530306,3582766049751239,16672702423031411,77587874702105452

%N Half the number of (n+1) X 4 binary arrays with no 2 X 2 subblock having exactly 2 ones.

%H R. H. Hardin, <a href="/A183776/b183776.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,18,-13,-70,24,64).

%F Empirical: a(n) = 2*a(n-1) + 18*a(n-2) - 13*a(n-3) - 70*a(n-4) + 24*a(n-5) + 64*a(n-6).

%F Empirical g.f.: (8 + 17*x - 49*x^2 - 82*x^3 + 66*x^4 + 88*x^5) / ((1 + 2*x)*(1 - 4*x - 10*x^2 + 33*x^3 + 4*x^4 - 32*x^5)). - _Colin Barker_, Apr 04 2018

%F The above g.f. is correct. See A183782 for bounds on the order of the recurrence. - _Andrew Howroyd_, Jan 09 2025

%e Some solutions with a(1,1)=0 for 3 X 4:

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

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

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

%Y Column k=3 of A183782.

%K nonn,easy

%O 0,1

%A _R. H. Hardin_, Jan 07 2011

%E a(0) prepended by _Andrew Howroyd_, Jan 09 2025