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A204679 Number of n X 2 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order. 3

%I #8 Feb 23 2018 09:51:30

%S 2,15,159,2191,31168,447343,6427791,92387812,1327953799,19087798375,

%T 274365294336,3943689122935,56686048473223,814797524429284,

%U 11711788424726319,168343648648695295,2419748633865949120

%N Number of n X 2 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

%C Column 2 of A204685.

%H R. H. Hardin, <a href="/A204679/b204679.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) +14*a(n-2) -124*a(n-3) -6*a(n-4) +90*a(n-5) -27*a(n-6) for n>8.

%F Empirical g.f.: x*(2 - 13*x - 79*x^2 + 3*x^3 + 140*x^4 - 57*x^5 - 21*x^6 + 9*x^7) / ((1 + x)*(1 + 3*x)*(1 - 3*x + x^2)*(1 - 15*x + 9*x^2)). - _Colin Barker_, Feb 23 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A204685.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 18 2012

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Last modified March 28 11:44 EDT 2024. Contains 371241 sequences. (Running on oeis4.)