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A230984 Number of white square subarrays of (n+1) X (3+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero. 2

%I #8 Mar 18 2018 06:22:57

%S 2,4,11,24,59,139,332,796,1903,4563,10934,26209,62835,150636,361156,

%T 865882,2076002,4977375,11933643,28611925,68599559,164473454,

%U 394339672,945464381,2266835107,5434939417,13030752556,31242393432,74906430076

%N Number of white square subarrays of (n+1) X (3+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero.

%C Column 3 of A230989.

%H R. H. Hardin, <a href="/A230984/b230984.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(2 - 3*x^2 - 4*x^3 + 2*x^4 + 2*x^5 - x^6) / (1 - 2*x - 3*x^2 + 3*x^3 + 6*x^4 - 2*x^5 - 4*x^6 + x^7 + x^8). - _Colin Barker_, Mar 18 2018

%e Some solutions for n=6:

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

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

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

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

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

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

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

%Y Cf. A230989.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 02 2013

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Last modified April 24 07:06 EDT 2024. Contains 371920 sequences. (Running on oeis4.)