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 A208114 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically. 1

%I #8 Jun 28 2018 08:42:24

%S 9,81,225,625,1225,2401,3969,6561,9801,14641,20449,28561,38025,50625,

%T 65025,83521,104329,130321,159201,194481,233289,279841,330625,390625,

%U 455625,531441,613089,707281,808201,923521,1046529,1185921,1334025

%N Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.

%C Column 4 of A208118.

%H R. H. Hardin, <a href="/A208114/b208114.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).

%F Conjectures from _Colin Barker_, Jun 28 2018: (Start)

%F G.f.: x*(9 + 63*x + 45*x^2 + 67*x^3 + 11*x^4 - 3*x^5 - x^6 + x^7) / ((1 - x)^5*(1 + x)^3).

%F a(n) = n^4 + 4*n^3 + 6*n^2 + 4*n + 1 for n even.

%F a(n) = n^4 + 4*n^3 + 4*n^2 for n odd.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208118.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 23 2012

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Last modified June 4 23:50 EDT 2023. Contains 363130 sequences. (Running on oeis4.)