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Number of n X 2 0..1 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.
2

%I #7 Mar 21 2018 09:40:11

%S 4,16,64,225,784,2601,8464,26896,84100,259081,788544,2374681,7086244,

%T 20976400,61653904,180069561,522945424,1510954641,4345446400,

%U 12444741136,35502850084,100926300721,285976813824,807886380625,2275928269924

%N Number of n X 2 0..1 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.

%C Column 2 of A267735.

%H R. H. Hardin, <a href="/A267729/b267729.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 19*a(n-3) + 24*a(n-4) + 24*a(n-5) - 19*a(n-6) - 6*a(n-7) + 6*a(n-8) - a(n-9).

%F Empirical g.f.: x*(4 - 8*x - 8*x^2 + 13*x^3 + 26*x^4 - 17*x^5 - 7*x^6 + 6*x^7 - x^8) / ((1 + x)^3*(1 - 3*x + x^2)^3). - _Colin Barker_, Mar 21 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A267735.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 20 2016