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A204638 Number of (n+2) X 6 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. 1

%I #9 Jun 08 2018 06:33:00

%S 4246,379,933,478,1169,4366,8179,29877,113861,407328,1541643,5847274,

%T 22096265,83765839,317588101,1203850602,4564121261,17303919222,

%U 65603484087,248721618481,942975306533,3575088842524,13554190638871

%N Number of (n+2) X 6 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 4 of A204642.

%H R. H. Hardin, <a href="/A204638/b204638.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*(4246 - 20851*x + 11776*x^2 + 13934*x^3 + 54046*x^4 - 42717*x^5 - 90750*x^6 + 31551*x^7 + 36801*x^8 + 504*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..1..0..0..2....0..0..0..1..1..1....0..0..0..1..1..1

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

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

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

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

%Y Cf. A204642.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 17 2012

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Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)