A205917 - OEIS

A205917

T(n,k) = number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock having the same number of clockwise edge increases as its horizontal neighbors and the same number of counterclockwise edge increases as its vertical neighbors.

%I #7 Dec 10 2015 02:08:30

%S 81,369,369,1764,1791,1764,8655,9831,9831,8655,43155,60108,87918,

%T 60108,43155,218034,387267,875760,875760,387267,218034,1112664,

%U 2554848,8986929,14150391,8986929,2554848,1112664,5722236,17051166,93488811,231526056

%N T(n,k) = number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock having the same number of clockwise edge increases as its horizontal neighbors and the same number of counterclockwise edge increases as its vertical neighbors.

%C Table starts

%C ......81.......369........1764..........8655...........43155............218034

%C .....369......1791........9831.........60108..........387267...........2554848

%C ....1764......9831.......87918........875760.........8986929..........93488811

%C ....8655.....60108......875760......14150391.......231526056........3820547082

%C ...43155....387267.....8986929.....231526056......6011669886......157611325827

%C ..218034...2554848....93488811....3820547082....157611325827.....6566654061039

%C .1112664..17051166...976932162...63265158237...4140502079766...274342874332980

%C .5722236.114537918.10250633343.1050303618804.109077858375072.11488530154756449

%H R. H. Hardin, <a href="/A205917/b205917.txt">Table of n, a(n) for n = 1..180</a>

%e Some solutions for n=4, k=3:

%e ..1..0..2..2....0..0..1..0....1..2..1..2....1..2..2..0....2..1..1..1

%e ..1..0..0..0....1..1..1..0....1..2..1..2....2..2..0..0....2..0..1..2

%e ..1..1..1..0....2..1..0..0....1..1..1..1....1..2..2..2....0..2..1..0

%e ..2..1..0..0....1..1..0..1....1..0..1..2....1..1..2..1....1..1..1..1

%e ..1..1..1..0....1..0..0..0....0..0..1..2....0..1..1..1....2..0..1..2

%Y Column 1 is A205737.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 01 2012