A204380 - OEIS

A204380

Number of (n+2) X 9 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..1 introduced in row major order.

%I #9 Jun 07 2018 11:47:05

%S 439,193,205,217,241,283,347,453,625,901,1349,2075,3247,5145,8217,

%T 13185,21225,34235,55283,89341,144449,233613,377885,611323,989031,

%U 1600177,2589033,4189033,6777889,10966747,17744459,28711029,46455313,75166165

%N Number of (n+2) X 9 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..1 introduced in row major order.

%C Column 7 of A204381.

%H R. H. Hardin, <a href="/A204380/b204380.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) for n>8.

%F Empirical g.f.: x*(439 - 246*x - 427*x^2 - 620*x^3 + 65*x^4 + 252*x^5 + 4*x^6 + 4*x^7) / ((1 - x)*(1 - x - x^2)*(1 + x + x^2)). - _Colin Barker_, Jun 07 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A204381.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 14 2012