A240460 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4

2, 4, 5, 8, 21, 12, 16, 89, 102, 28, 32, 375, 874, 476, 66, 64, 1583, 7589, 8187, 2200, 156, 128, 6685, 65723, 143237, 75167, 10123, 368, 256, 28241, 568370, 2501883, 2632690, 682018, 46471, 868, 512, 119319, 4916340, 43654661, 92193017, 47636104, 6147372

Offset

1,1

Comments

Table starts

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

....5......21.........89..........375..........1583...........6685

...12.....102........874.........7589.........65723.........568370

...28.....476.......8187.......143237.......2501883.......43654661

...66....2200......75167......2632690......92193017.....3228706651

..156...10123.....682018.....47636104....3337483054...234122685500

..368...46471....6147372....854671234..119643524281.16795323356869

..868..213000...55212526..15259447330.4265146133201

.2048..975380..494809053.271656519692

.4832.4464474.4428808128

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

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

k=2: [order 26]

Empirical for row n:

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

n=2: a(n) = 6*a(n-1) -7*a(n-2) -4*a(n-3) +8*a(n-4)

n=3: [order 23]

Example

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

Crossrefs

Column 1 is A239333

Row 1 is A000079

Sequence in context: A092061 A256760 A281646 * A239405 A097684 A344997

Adjacent sequences: A240457 A240458 A240459 * A240461 A240462 A240463

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 05 2014

Status

approved