A239405 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

2, 4, 5, 8, 23, 12, 16, 105, 129, 28, 32, 478, 1337, 698, 66, 64, 2165, 13977, 16449, 3805, 156, 128, 9811, 144762, 394509, 205969, 20818, 368, 256, 44399, 1504399, 9340070, 11334364, 2590704, 113774, 868, 512, 201006, 15591122, 222457036, 614216271

Offset

1,1

Comments

Table starts

....2.......4..........8............16................32...................64

....5......23........105...........478..............2165.................9811

...12.....129.......1337.........13977............144762..............1504399

...28.....698......16449........394509...........9340070............222457036

...66....3805.....205969......11334364.........614216271..........33522573911

..156...20818....2590704.....326882784.......40566958960........5072216819342

..368..113774...32507376....9402398952.....2671846338458......765206237815409

..868..621754..408000104..270516990628...176044655676921...115478426410506313

.2048.3399032.5124790809.7789048968124.11610439554314901.17442858177037612521

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: [order 16]

k=3: [order 64]

Empirical for row n:

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

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)

n=3: [order 25]

n=4: [order 91]

Example

Some solutions for n=3 k=4
..0..0..3..3....3..1..0..0....0..3..3..1....0..0..3..3....3..3..1..3
..0..0..0..2....0..0..3..3....3..3..0..2....3..3..0..2....0..3..2..0
..0..0..0..2....3..1..3..2....2..2..3..2....0..0..3..1....0..2..2..3

Crossrefs

Column 1 is A239333

Row 1 is A000079

Sequence in context: A256760 A281646 A240460 * A097684 A344997 A277289

Adjacent sequences: A239402 A239403 A239404 * A239406 A239407 A239408

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 17 2014

Status

approved