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A202197 Number of (n+2) X 5 binary arrays avoiding patterns 001 and 101 in rows and columns. 1

%I #13 May 27 2018 08:26:19

%S 450,1400,3500,7560,14700,26400,44550,71500,110110,163800,236600,

%T 333200,459000,620160,823650,1077300,1389850,1771000,2231460,2783000,

%U 3438500,4212000,5118750,6175260,7399350,8810200,10428400,12276000,14376560

%N Number of (n+2) X 5 binary arrays avoiding patterns 001 and 101 in rows and columns.

%C Column 3 of A202202.

%H R. H. Hardin, <a href="/A202197/b202197.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*(n+5)*(n+4)*(n+3)*(n+2)^2/12.

%F Conjectures from _Colin Barker_, May 27 2018: (Start)

%F G.f.: 10*x*(45 - 130*x + 185*x^2 - 144*x^3 + 59*x^4 - 10*x^5) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Cf. A202202.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 14 2011

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)