A241283 - OEIS

%I #4 Apr 18 2014 13:14:02

%S 2,3,4,4,3,10,7,5,9,24,10,13,41,36,56,15,17,126,236,139,132,24,35,224,

%T 773,1615,532,312,35,90,934,1800,6783,12356,2111,736,54,141,2741,

%U 16843,20717,77955,96171,8473,1736,83,288,5225,54167,451318,309657,1009773

%N T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4

%C Table starts

%C ....2......3........4..........7..........10............15...........24

%C ....4......3........5.........13..........17............35...........90

%C ...10......9.......41........126.........224...........934.........2741

%C ...24.....36......236........773........1800.........16843........54167

%C ...56....139.....1615.......6783.......20717........451318......1543713

%C ..132....532....12356......77955......309657......15616828.....60486552

%C ..312...2111....96171....1009773.....5423164.....730435588...2949336562

%C ..736...8473...761754...14440961...113305157...40083129145.193899487190

%C .1736..34053..6079503..217830879..2759021846.2390612565177

%C .4096.136880.48655224.3381893022.75062814060

%H R. H. Hardin, <a href="/A241283/b241283.txt">Table of n, a(n) for n = 1..111</a>

%F Empirical for column k:

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

%F k=2: [order 31]

%F Empirical for row n:

%F n=1: a(n)=a(n-2)+2*a(n-3)

%F n=2: [order 17] for n>18

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A052912

%Y Row 1 is A159288(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Apr 18 2014