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A202527 Number of (n+2) X 5 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals. 1

%I #8 Jun 01 2018 06:17:01

%S 417,1084,2263,4669,10240,22118,47098,101249,218000,467743,1004221,

%T 2157988,4635082,9954218,21381733,45927212,98644463,211878013,

%U 455096536,977499190,2099565274,4509660401,9686297296,20805178151,44687426189

%N Number of (n+2) X 5 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals.

%C Column 3 of A202532.

%H R. H. Hardin, <a href="/A202527/b202527.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +2*a(n-3) -2*a(n-4) -2*a(n-5) +a(n-7) for n>8.

%F Empirical g.f.: x*(417 + 250*x + 95*x^2 - 691*x^3 - 432*x^4 + 114*x^5 + 218*x^6 + 20*x^7) / ((1 - x)*(1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - _Colin Barker_, Jun 01 2018

%e Some solutions for n=3.

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

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

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

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

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

%Y Cf. A202532.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 20 2011

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Last modified July 17 10:44 EDT 2024. Contains 374377 sequences. (Running on oeis4.)