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A252956 Number of (n+2) X (3+2) 0..4 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order. 1

%I

%S 223,155,259,443,871,1681,2999,6103,11983,21749,44515,88087,161123,

%T 330817,656011,1210571,2483599,4939057,9174815,18819943,37462903,

%U 70101461,143554507,286165735,538738571,1101824353,2197577587,4162662491

%N Number of (n+2) X (3+2) 0..4 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

%H R. H. Hardin, <a href="/A252956/b252956.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 3*a(n-3) - 13*a(n-4) + 8*a(n-5) + 70*a(n-6) - 105*a(n-7) + 42*a(n-8) for n>10.

%F Empirical g.f.: x*(223 - 737*x + 85*x^2 + 386*x^3 + 2981*x^4 + 91*x^5 - 14137*x^6 + 16334*x^7 - 4830*x^8 - 420*x^9) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x^2)*(1 - 7*x^3)). - _Colin Barker_, Dec 07 2018

%e Some solutions for n=2:

%e ..0..1..1..2..2....0..1..1..2..2....0..1..1..0..1....0..1..1..2..2

%e ..3..0..0..1..1....3..0..0..4..4....0..2..0..0..2....3..0..0..1..1

%e ..2..4..4..0..4....2..3..3..1..1....0..0..2..0..0....2..3..3..0..0

%e ..1..3..3..4..3....4..2..2..0..0....0..1..1..0..1....1..4..4..3..3

%Y Column 3 of A252961.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 25 2014

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Last modified January 27 16:19 EST 2022. Contains 350608 sequences. (Running on oeis4.)