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A241283 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.

%I A241283 #6 Jun 02 2025 10:03:40
%S A241283 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 A241283 773,1615,532,312,35,90,934,1800,6783,12356,2111,736,54,141,2741,
%U A241283 16843,20717,77955,96171,8473,1736,83,288,5225,54167,451318,309657,1009773
%N A241283 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 A241283 Table starts
%C A241283 ....2......3........4..........7..........10............15...........24
%C A241283 ....4......3........5.........13..........17............35...........90
%C A241283 ...10......9.......41........126.........224...........934.........2741
%C A241283 ...24.....36......236........773........1800.........16843........54167
%C A241283 ...56....139.....1615.......6783.......20717........451318......1543713
%C A241283 ..132....532....12356......77955......309657......15616828.....60486552
%C A241283 ..312...2111....96171....1009773.....5423164.....730435588...2949336562
%C A241283 ..736...8473...761754...14440961...113305157...40083129145.193899487190
%C A241283 .1736..34053..6079503..217830879..2759021846.2390612565177
%C A241283 .4096.136880.48655224.3381893022.75062814060
%H A241283 R. H. Hardin, <a href="/A241283/b241283.txt">Table of n, a(n) for n = 1..111</a>
%F A241283 Empirical for column k:
%F A241283 k=1: a(n) = 2*a(n-1) +2*a(n-3)
%F A241283 k=2: [order 31]
%F A241283 Empirical for row n:
%F A241283 n=1: a(n)=a(n-2)+2*a(n-3)
%F A241283 n=2: [order 17] for n>18
%e A241283 Some solutions for n=4 k=4
%e A241283 ..3..3..2..3....3..2..3..2....3..2..3..2....3..3..2..3....3..3..2..3
%e A241283 ..2..1..1..0....0..3..2..3....2..1..2..3....2..1..3..2....2..1..1..0
%e A241283 ..2..2..0..0....2..0..2..0....0..0..2..0....3..1..2..2....2..2..2..2
%e A241283 ..2..0..0..2....0..0..0..3....2..0..2..0....3..2..1..2....2..0..0..2
%Y A241283 Column 1 is A052912
%Y A241283 Row 1 is A159288(n+1)
%K A241283 nonn,tabl
%O A241283 1,1
%A A241283 _R. H. Hardin_, Apr 18 2014