A239405 - OEIS

%I #6 Jun 02 2025 09:27:48

%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