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 A220574 Equals one maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 n X 3 array. 1

%I #7 Aug 01 2018 04:56:13

%S 4,21,91,375,1487,5835,22775,88683,344975,1341395,5214791,20271307,

%T 78797247,306290211,1190562423,4627750267,17988173039,69920406547,

%U 271782019879,1056422029931,4106332901663,15961395217283,62042250575063

%N Equals one maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 n X 3 array.

%C Column 3 of A220579.

%H R. H. Hardin, <a href="/A220574/b220574.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 4*a(n-2) + 2*a(n-3) - 12*a(n-4) - 16*a(n-5) for n>6.

%F Empirical g.f.: x*(4 + 9*x + 12*x^2 + 10*x^3 + 4*x^4 + 8*x^5) / (1 - 3*x - 4*x^2 - 2*x^3 + 12*x^4 + 16*x^5). - _Colin Barker_, Aug 01 2018

%e Some solutions for n=3:

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

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

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

%Y Cf. A220579.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 16 2012

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Last modified August 15 00:19 EDT 2024. Contains 375171 sequences. (Running on oeis4.)