A184542 - OEIS

%I #8 Apr 13 2018 08:45:54

%S 147,340,631,1048,1627,2413,3461,4837,6619,8898,11779,15382,19843,

%T 25315,31969,39995,49603,61024,74511,90340,108811,130249,155005,

%U 183457,216011,253102,295195,342786,396403,456607,523993,599191,682867,775724,878503

%N Number of (n+2) X 5 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

%C Column 3 of A184548.

%H R. H. Hardin, <a href="/A184542/b184542.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (1/120)*n^5 + (5/24)*n^4 + (49/24)*n^3 + (739/24)*n^2 + (1659/20)*n + 31.

%F Conjectures from _Colin Barker_, Apr 13 2018: (Start)

%F G.f.: x*(147 - 542*x + 796*x^2 - 578*x^3 + 209*x^4 - 31*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>5.

%F (End)

%e Some solutions for 4 X 5:

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

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

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

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

%Y Cf. A184548.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 16 2011