A239405 - OEIS

%I #4 Mar 17 2014 17:46:54

%S 2,4,5,8,23,12,16,105,129,28,32,478,1337,698,66,64,2165,13977,16449,

%T 3805,156,128,9811,144762,394509,205969,20818,368,256,44399,1504399,

%U 9340070,11334364,2590704,113774,868,512,201006,15591122,222457036,614216271

%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, modulo 4

%C Table starts

%C ....2.......4..........8............16................32...................64

%C ....5......23........105...........478..............2165.................9811

%C ...12.....129.......1337.........13977............144762..............1504399

%C ...28.....698......16449........394509...........9340070............222457036

%C ...66....3805.....205969......11334364.........614216271..........33522573911

%C ..156...20818....2590704.....326882784.......40566958960........5072216819342

%C ..368..113774...32507376....9402398952.....2671846338458......765206237815409

%C ..868..621754..408000104..270516990628...176044655676921...115478426410506313

%C .2048.3399032.5124790809.7789048968124.11610439554314901.17442858177037612521

%H R. H. Hardin, <a href="/A239405/b239405.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: [order 16]

%F k=3: [order 64]

%F Empirical for row n:

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

%F n=2: a(n) = 3*a(n-1) +12*a(n-2) -18*a(n-3) -29*a(n-4) +19*a(n-5) +38*a(n-6) +8*a(n-7)

%F n=3: [order 25]

%F n=4: [order 91]

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A239333

%Y Row 1 is A000079

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 17 2014