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A207701 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically. 1

%I

%S 25,625,3969,15129,43681,105625,225625,439569,797449,1366561,2235025,

%T 3515625,5349969,7912969,11417641,16120225,22325625,30393169,40742689,

%U 53860921,70308225,90725625,115842169,146482609,183575401,228161025

%N Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.

%C Column 6 of A207703.

%H R. H. Hardin, <a href="/A207701/b207701.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

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

%F G.f.: x*(25 + 450*x + 119*x^2 - 404*x^3 + 127*x^4 + 2*x^5 + x^6) / (1 - x)^7.

%F a(n) = (-3 + n + 15*n^2 + 2*n^3)^2 / 9.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A207703.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 19 2012

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Last modified October 16 06:14 EDT 2021. Contains 348040 sequences. (Running on oeis4.)