A202048 - OEIS

%I #10 May 25 2018 12:21:27

%S 636,1968,4980,11016,22092,41088,71964,120000,192060,296880,445380,

%T 651000,930060,1302144,1790508,2422512,3230076,4250160,5525268,

%U 7103976,9041484,11400192,14250300,17670432,21748284,26581296,32277348,38955480

%N Number of (n+2) X 6 binary arrays avoiding patterns 001 and 110 in rows and columns.

%C Column 4 of A202052.

%H R. H. Hardin, <a href="/A202048/b202048.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/30)*n^6 + (9/10)*n^5 + (59/6)*n^4 + (111/2)*n^3 + (2552/15)*n^2 + (1278/5)*n + 144.

%F Conjectures from _Colin Barker_, May 25 2018: (Start)

%F G.f.: 12*x*(53 - 207*x + 380*x^2 - 398*x^3 + 245*x^4 - 83*x^5 + 12*x^6) / (1 - x)^7.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A202052.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 10 2011