A204368 - OEIS

A204368

Number of (n+2) X 8 0..2 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..2 introduced in row major order.

%I #8 Jun 07 2018 08:28:50

%S 6121,4355,2574,2956,3280,4856,9272,19880,50056,132856,356056,968312,

%T 2641688,7207448,19686232,53780248,146914840,401373080,1096568600,

%U 2995854104,8184818200,22361337112,61092259096,166907144984,455998800152

%N Number of (n+2) X 8 0..2 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..2 introduced in row major order.

%C Column 6 of A204370.

%H R. H. Hardin, <a href="/A204368/b204368.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>9.

%F Empirical g.f.: x*(6121 - 14008*x - 10491*x^2 - 4766*x^3 + 31138*x^4 + 21146*x^5 - 14336*x^6 - 7620*x^7 - 200*x^8) / ((1 - x)*(1 - 2*x - 2*x^2)*(1 - 2*x^3)). - _Colin Barker_, Jun 07 2018

%e Some solutions for n=5:

%e ..0..1..2..0..1..0..1..2....0..1..0..0..1..1..0..0....0..0..1..2..1..2..2..2

%e ..0..1..2..0..1..0..1..2....0..1..0..0..1..1..0..0....0..0..1..2..1..2..2..1

%e ..0..1..2..0..1..0..1..2....0..0..0..0..1..1..0..0....0..0..1..2..1..2..2..1

%e ..0..1..2..0..1..0..1..2....2..1..0..0..1..1..0..0....0..0..1..2..1..2..2..1

%Y Cf. A204370.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 14 2012