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: A389429 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