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Number of nX7 n X 7 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.

Column 7 of A275142.

Empirical: a(n) = 3*a(n-1) + 18*a(n-2) + 11*a(n-3) - 23*a(n-4) - 4*a(n-5) for n>7.

Empirical g.f.: 16*x*(2 + 75*x - 103*x^2 - 891*x^3 - 647*x^4 + 1172*x^5 + 144*x^6) / (1 - 3*x - 18*x^2 - 11*x^3 + 23*x^4 + 4*x^5). - Colin Barker, Jan 31 2019

Some solutions for n=5:

Cf. Column 7 of A275142.

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R. H. Hardin, <a href="/A275141/b275141.txt">Table of n, a(n) for n = 1..210</a>

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Number of nX7 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.

32, 1296, 2816, 17872, 107472, 663904, 4055152, 24875600, 152379136, 933805200, 5721947536, 35062147296, 214849132208, 1316520434704, 8067189289984, 49432958970960, 302908230284368, 1856117667993184, 11373652262370288

1,1

Column 7 of A275142.

Empirical: a(n) = 3*a(n-1) +18*a(n-2) +11*a(n-3) -23*a(n-4) -4*a(n-5) for n>7

Some solutions for n=5

..0..1..0..2..1..2..0. .0..1..2..0..1..2..0. .0..1..0..2..0..1..0

..0..2..1..0..2..1..2. .2..0..1..2..0..1..0. .0..2..1..0..1..0..1

..1..2..1..0..2..1..0. .2..0..1..2..0..1..2. .1..0..1..0..2..1..2

..1..0..2..1..2..1..0. .1..0..1..2..0..1..2. .2..0..2..1..2..1..0

..2..1..2..1..0..2..1. .0..1..0..1..0..1..2. .0..1..0..2..0..2..1

Cf. A275142.

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R. H. Hardin, Jul 17 2016

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