A204639 - OEIS

A204639

Number of (n+2) X 7 0..3 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..3 introduced in row major order.

%I #8 Jun 08 2018 06:32:53

%S 16855,1860,760,1169,3300,3077,9482,35500,109224,410467,1557742,

%T 5832593,22104912,83813366,317543288,1203875773,4564263072,

%U 17303784013,65603558830,248722043144,942974900136,3575089065983,13554191912090

%N Number of (n+2) X 7 0..3 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..3 introduced in row major order.

%C Column 5 of A204642.

%H R. H. Hardin, <a href="/A204639/b204639.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) -3*a(n-2) -4*a(n-3) -12*a(n-4) +12*a(n-5) +21*a(n-6) -9*a(n-7) -9*a(n-8) for n>10.

%F Empirical g.f.: x*(16855 - 82415*x + 42025*x^2 + 70369*x^3 + 209435*x^4 - 186816*x^5 - 358482*x^6 + 128064*x^7 + 150525*x^8 + 5130*x^9) / ((1 - x)*(1 - x - x^2)*(1 - 3*x - 3*x^2)*(1 - 3*x^3)). - _Colin Barker_, Jun 08 2018

%e Some solutions for n=3:

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

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

%e ..1..1..1..1..1..1..1....0..0..1..0..1..2..0....2..2..2..0..0..0..3

%e ..2..2..2..2..2..2..2....0..0..1..0..1..2..0....2..2..0..0..0..3..3

%e ..1..1..1..1..1..1..1....0..0..1..0..1..2..0....2..0..0..0..3..3..3

%Y Cf. A204642.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 17 2012