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 A202440 Number of (n+2) X 3 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals. 1

%I #10 May 28 2018 18:25:55

%S 80,138,224,338,484,666,888,1154,1468,1834,2256,2738,3284,3898,4584,

%T 5346,6188,7114,8128,9234,10436,11738,13144,14658,16284,18026,19888,

%U 21874,23988,26234,28616,31138,33804,36618,39584,42706,45988,49434,53048,56834

%N Number of (n+2) X 3 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.

%C Column 1 of A202447.

%H R. H. Hardin, <a href="/A202440/b202440.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (2/3)*n^3 + 8*n^2 + (100/3)*n + 34 for n>1.

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

%F G.f.: 2*x*(40 - 91*x + 76*x^2 - 25*x^3 + 2*x^4) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Cf. A202447.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2011

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Last modified May 29 00:59 EDT 2023. Contains 363029 sequences. (Running on oeis4.)