A204753 - OEIS

A204753

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

%I #10 Jun 10 2018 20:47:09

%S 1051,70,69,74,82,95,116,150,205,294,438,671,1048,1658,2645,4242,6826,

%T 11007,17772,28718,46429,75086,121454,196479,317872,514290,832101,

%U 1346330,2178370,3524639,5702948,9227526,14930413,24157878,39088230

%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, diagonally or antidiagonally exactly three ways, and new values 0..1 introduced in row major order.

%C Column 7 of A204754.

%H R. H. Hardin, <a href="/A204753/b204753.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(1051 - 2032*x - 71*x^2 + 987*x^3 + 4*x^4) / ((1 - x)*(1 - x - x^2)). - _Colin Barker_, Jun 10 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A204754.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 18 2012