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A230937 Number of white-square subarrays of (n+2) X (3+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero. 1

%I #8 Sep 24 2018 02:48:02

%S 2,16,34,232,522,3768,8450,60824,136474,982552,2204498,15870936,

%T 35608874,256361112,575185186,4140964568,9290884794,66888415128,

%U 150074347890,1080439106264,2424129709770,17452180031640,39156624254530

%N Number of white-square subarrays of (n+2) X (3+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.

%H R. H. Hardin, <a href="/A230937/b230937.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-2) +3*a(n-4) -10*a(n-6) +24*a(n-8) -16*a(n-10).

%F Empirical g.f.: 2*x*(1 + 8*x + x^2 - 12*x^3 - 14*x^4 + 4*x^5 + 8*x^6) / (1 - 16*x^2 - 3*x^4 + 10*x^6 - 24*x^8 + 16*x^10). - _Colin Barker_, Sep 23 2018

%e Some solutions for n=4:

%e ..0..x..0..x..0....0..x..2..x..2....0..x..2..x..2....0..x..2..x..2

%e ..x..1..x..1..x....x..1..x..3..x....x..1..x..3..x....x..1..x..3..x

%e ..0..x..2..x..0....2..x..0..x..2....0..x..0..x..2....0..x..0..x..0

%e ..x..1..x..3..x....x..3..x..1..x....x..3..x..3..x....x..3..x..1..x

%e ..0..x..2..x..2....2..x..0..x..0....2..x..2..x..2....0..x..2..x..0

%e ..x..1..x..1..x....x..1..x..3..x....x..1..x..1..x....x..1..x..3..x

%Y Column 3 of A230940.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 01 2013

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Last modified May 21 01:24 EDT 2024. Contains 372720 sequences. (Running on oeis4.)