%I #4 Apr 04 2014 10:18:08
%S 2,4,4,8,15,7,16,51,43,11,32,188,257,111,16,64,672,1693,1181,261,22,
%T 128,2452,10997,13846,4825,571,29,256,8822,74255,165110,99412,18307,
%U 1171,37,512,32077,492758,2057843,2150725,663122,64013,2278,46,1024,115811
%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 two plus the sum of the elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4
%C Table starts
%C ..2....4.......8........16..........32...........64...........128...........256
%C ..4...15......51.......188.........672.........2452..........8822.........32077
%C ..7...43.....257......1693.......10997........74255........492758.......3349106
%C .11..111....1181.....13846......165110......2057843......25667276.....329976721
%C .16..261....4825.....99412.....2150725.....49010279....1144026966...27661711340
%C .22..571...18307....663122....25831820...1069763402...46251359120.2092454198295
%C .29.1171...64013...4069449...285724643..21520521111.1718692144996
%C .37.2278..209366..23273667..2936736845.402124337377
%C .46.4235..645067.125118158.28324834725
%C .56.7570.1889163.638885869
%H R. H. Hardin, <a href="/A240364/b240364.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
%F k=2: [polynomial of degree 8] for n>4
%F k=3: [polynomial of degree 26] for n>18
%F k=4: [polynomial of degree 80] for n>61
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1)
%F n=2: [linear recurrence of order 12]
%F n=3: [order 80]
%e Some solutions for n=4 k=4
%e ..0..0..0..3....3..3..0..0....0..3..3..0....0..0..0..0....0..0..0..0
%e ..3..3..0..0....3..3..0..0....0..0..0..3....0..3..1..3....0..3..1..0
%e ..3..2..0..3....3..2..3..3....0..0..0..2....3..3..2..0....3..3..0..1
%e ..3..2..0..3....0..3..2..0....3..3..0..0....0..3..3..2....3..3..0..0
%Y Column 1 is A000124
%Y Row 1 is A000079
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Apr 04 2014