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Number of n X 2 (0,1,2) arrays of permanents of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
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%I #7 Sep 06 2018 11:30:19

%S 7,26,72,171,368,729,1343,2325,3819,6001,9082,13311,18978,26417,36009,

%T 48185,63429,82281,105340,133267,166788,206697,253859,309213,373775,

%U 448641,534990,634087,747286,876033,1021869,1186433,1371465,1578809

%N Number of n X 2 (0,1,2) arrays of permanents of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.

%H R. H. Hardin, <a href="/A227021/b227021.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40)*n^5 + (1/3)*n^4 - (1/8)*n^3 + (5/3)*n^2 + (141/10)*n - 15 for n>2.

%F Conjectures from _Colin Barker_, Sep 06 2018: (Start)

%F G.f.: x*(7 - 16*x + 21*x^2 - 11*x^3 + 7*x^4 - 6*x^5 + x^7) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=4:

%e ..0..0....0..0....0..1....1..2....0..1....0..0....0..1....0..0....0..0....1..1

%e ..0..1....0..1....0..0....2..2....0..0....0..0....1..0....0..2....1..1....1..1

%e ..2..1....0..0....0..0....2..2....1..0....1..2....1..0....0..2....0..0....2..1

%e ..2..2....1..1....1..0....2..2....0..0....2..2....2..0....0..2....0..0....2..2

%Y Column 2 of A227025.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 27 2013