A240284 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4

1, 2, 2, 2, 8, 3, 4, 19, 19, 4, 4, 76, 80, 38, 7, 8, 181, 570, 262, 114, 10, 8, 741, 2574, 3457, 1461, 251, 15, 16, 1779, 20764, 28654, 33183, 5443, 612, 24, 16, 7308, 97348, 443168, 484146, 218658, 24490, 1656, 35, 32, 17561, 802835, 3980245, 13490093, 5646644

Offset

1,2

Comments

Table starts

..1....2.......2.........4............4.............8..............8

..2....8......19........76..........181...........741...........1779

..3...19......80.......570.........2574.........20764..........97348

..4...38.....262......3457........28654........443168........3980245

..7..114....1461.....33183.......484146......13490093......224906182

.10..251....5443....218658......5646644.....281488213.....8597299482

.15..612...24490...1851080.....88953626....8199368365...463717321235

.24.1656..117962..15760838...1357879302..225885684501.23104690637116

.35.3758..459193.110599613..17350066110.5291794810655

.54.9630.2147788.945852472.272318368893

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical for column k:

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

k=2: [order 15]

Empirical for row n:

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

n=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)

n=3: [order 48] for n>51

Example

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

Crossrefs

Column 1 is A159288

Row 1 is A016116

Sequence in context: A054271 A278245 A321026 * A344897 A011202 A085484

Adjacent sequences: A240281 A240282 A240283 * A240285 A240286 A240287

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 03 2014

Status

approved