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%I #8 Jul 19 2023 10:19:23
%S 258,844,3264,11792,41125,146033,518500,1829248,6456790,22804970,
%T 80487561,284029242,1002372834,3537239577,12482044458,44046176233,
%U 155426964450,548457225605,1935348475463,6829275410361,24098489355181
%N Number of (n+2)X4 binary arrays avoiding patterns 001 and 010 in rows, columns and nw-to-se diagonals.
%H R. H. Hardin, <a href="/A202892/b202892.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) -15*a(n-2) +51*a(n-3) -146*a(n-4) +236*a(n-5) -502*a(n-6) +942*a(n-7) -805*a(n-8) +1335*a(n-9) -1767*a(n-10) -758*a(n-11) -701*a(n-12) +972*a(n-13) +5841*a(n-14) +1878*a(n-15) -2262*a(n-16) -9338*a(n-17) -8614*a(n-18) +3129*a(n-19) +12283*a(n-20) +12775*a(n-21) +1994*a(n-22) -12403*a(n-23) -13073*a(n-24) -4954*a(n-25) +6289*a(n-26) +9875*a(n-27) +4484*a(n-28) -1723*a(n-29) -4199*a(n-30) -2545*a(n-31) +8*a(n-32) +1153*a(n-33) +603*a(n-34) +228*a(n-35) -181*a(n-36) -76*a(n-37) -12*a(n-38) -19*a(n-39) +16*a(n-40) -8*a(n-41) +4*a(n-42) for n>43.
%e Some solutions for n=3
%e ..0..1..1..0....0..1..1..1....0..1..1..0....1..1..1..1....1..1..1..1
%e ..1..1..1..1....1..1..1..1....1..1..0..0....0..1..1..0....1..1..1..1
%e ..1..1..1..1....1..1..1..0....1..1..1..0....1..1..1..1....1..1..0..0
%e ..1..1..0..1....1..0..0..0....0..1..1..0....1..0..1..1....1..1..1..0
%e ..0..1..1..0....1..1..1..0....0..0..0..0....1..1..0..1....0..1..1..0
%Y Column 2 of A202898.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 25 2011