A230928 - OEIS

%I #8 Mar 17 2018 07:10:05

%S 2,2,8,8,42,42,208,208,1042,1042,5208,5208,26042,26042,130208,130208,

%T 651042,651042,3255208,3255208,16276042,16276042,81380208,81380208,

%U 406901042,406901042,2034505208,2034505208,10172526042,10172526042

%N Number of black-square subarrays of (n+2) X (1+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.

%C Column 1 of A230935.

%H R. H. Hardin, <a href="/A230928/b230928.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-2) + 5*a(n-4).

%F Empirical g.f.: 2*x*(1 + x) / ((1 + x^2)*(1 - 5*x^2)). - _Colin Barker_, Mar 17 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Cf. A230935.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 01 2013