login
Number of 2 X n 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
16

%I #14 Feb 17 2018 20:29:33

%S 4,16,36,81,196,441,961,2116,4624,10000,21609,46656,100489,216225,

%T 465124,1000000,2149156,4618201,9922500,21316689,45792289,98366724,

%U 211295296,453860416,974875729,2093977600,4497714225,9660727521,20750402500

%N Number of 2 X n 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

%C Row 2 of A207068.

%H R. H. Hardin, <a href="/A207069/b207069.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 3*a(n-3) - 6*a(n-4) + 3*a(n-7) + a(n-8) - a(n-10).

%F Empirical g.f.: x*(4 + 4*x - 4*x^2 - 7*x^3 + x^4 + 3*x^5 + 3*x^6 + x^7 - x^8 - x^9) / ((1 - x)*(1 + x^2 - x^3)*(1 - x - x^3)*(1 - x - 2*x^2 - x^3)). - _Colin Barker_, Feb 17 2018

%e Some solutions for n=4:

%e 1 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0

%e 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 14 2012