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A202456 Number of (n+2) X 5 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column. 1

%I

%S 1000,1876,3362,5735,9338,14586,21972,32073,45556,63184,85822,114443,

%T 150134,194102,247680,312333,389664,481420,589498,715951,862994,

%U 1033010,1228556,1452369,1707372,1996680,2323606,2691667,3104590,3566318,4081016

%N Number of (n+2) X 5 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.

%C Column 3 of A202461.

%H R. H. Hardin, <a href="/A202456/b202456.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/20)*n^5 + 2*n^4 + (275/12)*n^3 + 113*n^2 + (10351/30)*n + 517.

%F Conjectures from _Colin Barker_, May 31 2018: (Start)

%F G.f.: x*(1000 - 4124*x + 7106*x^2 - 6297*x^3 + 2838*x^4 - 517*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 ..0..0..0..0..0....0..0..0..1..0....0..0..0..0..0....0..0..0..0..0

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

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

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

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

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

%Y Cf. A202461.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2011

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Last modified September 19 00:22 EDT 2021. Contains 347549 sequences. (Running on oeis4.)