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A253227 Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically. 1

%I

%S 335,742,914,1498,2543,4490,8216,15476,29780,58148,114620,227276,

%T 452276,901940,1800908,3598460,7193156,14382116,28759580,57514028,

%U 115022420,230038676,460070636,920133980,1840260068,3680511620,7361014076

%N Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically.

%H R. H. Hardin, <a href="/A253227/b253227.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>8.

%F Conjectures from _Colin Barker_, Dec 10 2018: (Start)

%F G.f.: x*(335 - 933*x + 219*x^2 + 1261*x^3 - 1245*x^4 + 343*x^5 - 5*x^6 + x^7) / ((1 - x)^3*(1 - 2*x)).

%F a(n) = 188 + 1755*2^(n-5) + 60*n + 12*n^2 for n>4.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 4 of A253231.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2014

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Last modified August 8 20:31 EDT 2022. Contains 356016 sequences. (Running on oeis4.)