|
%I #9 Jun 08 2018 06:32:32
%S 1781,5974,248,933,760,2517,9750,28856,108520,412247,1538786,5831457,
%T 22111228,83757474,317540856,1203895697,4564096372,17303777693,
%U 65603619578,248721544020,942974882152,3575089249203,13554190415694
%N Number of (n+2) X 5 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 3 of A204642.
%H R. H. Hardin, <a href="/A204637/b204637.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*(1781 - 2931*x - 24279*x^2 + 24739*x^3 + 42107*x^4 + 52824*x^5 - 102936*x^6 - 110508*x^7 + 66069*x^8 + 52704*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..1..1....0..0..1..1..0....0..0..0..1..1....0..1..1..2..0
%e ..2..0..0..0..2....0..0..1..1..0....1..0..0..0..1....0..1..1..2..0
%e ..2..2..0..0..0....0..0..1..1..0....1..1..0..0..0....0..1..1..2..0
%e ..2..2..2..0..0....0..0..1..1..0....1..1..1..0..0....0..1..1..2..0
%e ..1..2..2..2..0....0..0..1..1..0....0..1..1..1..0....0..1..1..2..0
%Y Cf. A204642.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 17 2012
| 