A231441 - OEIS

A231441

T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order

%I #4 Nov 09 2013 06:24:03

%S 1,2,2,3,4,3,6,8,8,6,11,17,21,17,11,23,45,54,54,45,23,47,104,185,182,

%T 185,104,47,102,280,561,820,820,561,280,102,221,752,1943,3071,4450,

%U 3071,1943,752,221,492,2076,6756,13458,21472,21472,13458,6756,2076,492,1099,5947

%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order

%C Table starts

%C ...1....2.....3.......6.......11.......23.......47......102.......221.......492

%C ...2....4.....8......17.......45......104......280......752......2076......5947

%C ...3....8....21......54......185......561.....1943.....6756.....24003.....88488

%C ...6...17....54.....182......820.....3071....13458....59480....266481...1252868

%C ..11...45...185.....820.....4450....21472...117959...653280...3702873..21843997

%C ..23..104...561....3071....21472...133646...919000..6530487..46899990.351910410

%C ..47..280..1943...13458...117959...919000..7859324.70278737.631712523

%C .102..752..6756...59480...653280..6530487.70278737

%C .221.2076.24003..266481..3702873.46899990

%C .492.5947.88488.1252868.21843997

%H R. H. Hardin, <a href="/A231441/b231441.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +a(n-4) +3*a(n-5)

%F k=2: [order 19]

%F k=3: [order 24]

%e Some solutions for n=5 k=4

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

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

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

%e ..2..2..3..3..2..2....2..2..1..1..3..3....2..2..0..0..1..1....1..1..1..1..1..1

%e ..3..3..3..3..3..3....2..2..2..3..3..3....2..2..2..0..0..0....0..0..1..1..0..0

%e ..3..3..3..3..3..3....2..2..2..3..3..3....2..2..2..0..0..0....0..0..0..0..0..0

%Y Column 1 is A199142(n+2)

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 09 2013