login
Number of (n+2) X (1+2) 0..2 arrays with each 3 X 3 subblock having the sum of its 72 absolute element differences equal to 34 and no adjacent elements equal.
1

%I #8 Oct 16 2018 11:25:06

%S 56,88,138,176,312,432,584,960,1408,1872,3168,4544,6080,10176,14720,

%T 19648,33024,47616,63616,106752,154112,205824,345600,498688,666112,

%U 1118208,1613824,2155520,3618816,5222400,6975488,11710464,16900096

%N Number of (n+2) X (1+2) 0..2 arrays with each 3 X 3 subblock having the sum of its 72 absolute element differences equal to 34 and no adjacent elements equal.

%H R. H. Hardin, <a href="/A234927/b234927.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 2*x*(28 + 44*x + 69*x^2 + 32*x^3 + 68*x^4 + 78*x^5 + 4*x^6 - 8*x^7 - 4*x^8) / (1 - 2*x^3 - 4*x^6). - _Colin Barker_, Oct 16 2018

%e Some solutions for n=5:

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 01 2014