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A204640 Number of (n+2) X 8 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 #8 Jun 08 2018 06:32:46

%S 65096,2239,2517,4366,3077,5446,16171,31929,113429,427632,1544127,

%T 5842306,22153505,83769619,317569525,1204018650,4564128929,

%U 17303859822,65603984559,248721637813,942975124661,3575090340268,13554190693195

%N Number of (n+2) X 8 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 6 of A204642.

%H R. H. Hardin, <a href="/A204640/b204640.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*(65096 - 323241*x + 186610*x^2 + 258882*x^3 + 778906*x^4 - 741057*x^5 - 1348044*x^6 + 540753*x^7 + 561771*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..1..0..0..1..1..0..1....0..1..1..0..2..0..2..1....0..0..0..0..0..0..0..0

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

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

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

%e ..0..1..0..0..1..1..0..1....0..1..1..0..2..0..2..1....0..0..0..0..0..0..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 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)