A240046 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4

2, 2, 2, 4, 4, 4, 6, 9, 10, 6, 8, 20, 26, 22, 8, 14, 33, 72, 93, 50, 14, 20, 76, 174, 346, 309, 119, 20, 30, 117, 597, 1110, 1496, 1043, 276, 30, 48, 232, 1187, 5780, 7514, 8567, 3597, 637, 48, 70, 398, 3115, 17297, 55034, 61858, 46381, 12865, 1473, 70, 108, 675, 7269

Offset

1,1

Comments

Table starts

..2....2......4.......6.........8..........14..........20..........30

..2....4......9......20........33..........76.........117.........232

..4...10.....26......72.......174.........597........1187........3115

..6...22.....93.....346......1110........5780.......17297.......57800

..8...50....309....1496......7514.......55034......236282.....1248277

.14..119...1043....8567.....61858......640643.....4593632....35084947

.20..276...3597...46381....515675.....8300260...104619164..1204711882

.30..637..12865..268672...4743056...119956268..2789729009.49892724623

.48.1473..45491.1556758..45158204..1944727891.80805084589

.70.3355.163686.9438166.453408919.34311716212

Links

R. H. Hardin, Table of n, a(n) for n = 1..126

Formula

Empirical for column k:

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

k=2: [order 38] for n>40

Empirical for row n:

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

n=2: [order 18] for n>22

n=3: [order 76] for n>96

Example

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

Crossrefs

Row and Column 1 are A239851

Sequence in context: A007294 A053282 A218084 * A363947 A001584 A180019

Adjacent sequences: A240043 A240044 A240045 * A240047 A240048 A240049

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 31 2014

Status

approved