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A252725 Number of (6+2) X (n+2) 0..3 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 #7 Dec 06 2018 07:49:41

%S 165,154,170,178,214,262,270,354,434,466,622,790,846,1170,1490,1618,

%T 2254,2902,3150,4434,5714,6226,8782,11350,12366,17490,22610,24658,

%U 34894,45142,49230,69714,90194,98386,139342,180310,196686,278610,360530,393298

%N Number of (6+2) X (n+2) 0..3 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="/A252725/b252725.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = -a(n-1) +3*a(n-3) +3*a(n-4) -2*a(n-6) -2*a(n-7) for n>9.

%F Empirical g.f.: x*(165 + 319*x + 324*x^2 - 147*x^3 - 565*x^4 - 496*x^5 - 182*x^6 + 86*x^7 + 8*x^8) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 - 2*x^3)). - _Colin Barker_, Dec 06 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

%Y Row 6 of A252719.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 20 2014

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)