A240792 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4

2, 3, 3, 4, 4, 4, 7, 5, 5, 7, 10, 10, 8, 10, 10, 15, 14, 19, 27, 13, 15, 24, 24, 34, 37, 49, 14, 24, 35, 53, 82, 132, 85, 50, 30, 35, 54, 70, 278, 552, 460, 142, 89, 32, 54, 83, 140, 669, 2277, 2009, 1130, 386, 115, 36, 83, 124, 237, 1969, 11588, 15611, 6993, 6393, 979, 182

Offset

1,1

Comments

Table starts

..2..3...4....7.....10......15.........24.........35..........54.........83

..3..4...5...10.....14......24.........53.........70.........140........237

..4..5...8...19.....34......82........278........669........1969.......3553

..7.10..27...37....132.....552.......2277......11588.......35799.....109054

.10.13..49...85....460....2009......15611......90831......522104....2386511

.15.14..50..142...1130....6993......92681.....983289.....7075546...64616034

.24.30..89..386...6393...69732....1691066...33021579...408482271.5524873850

.35.32.115..979..22255..398128...16946464..651434319.13673101597

.54.36.182.1988..62705.1646410..117913446.8338435721

.83.67.289.5128.252760.9472037.1022475213

Links

R. H. Hardin, Table of n, a(n) for n = 1..142

Formula

Empirical for column k:

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

k=2: [order 17] for n>19

k=3: [order 76] for n>87

Empirical for row n:

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

n=2: [order 17] for n>21

Example

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

Crossrefs

Row and column 1 are A159288(n+1)

Sequence in context: A209727 A063123 A086333 * A367129 A360745 A217121

Adjacent sequences: A240789 A240790 A240791 * A240793 A240794 A240795

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 12 2014

Status

approved