A241435 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 one plus the sum of the elements antidiagonally to its northeast, modulo 4.

2, 3, 3, 4, 5, 4, 7, 10, 2, 7, 10, 21, 22, 3, 10, 15, 45, 74, 97, 5, 15, 24, 88, 158, 515, 213, 6, 24, 35, 181, 448, 1563, 1527, 381, 9, 35, 54, 378, 1272, 5915, 7495, 5304, 1005, 10, 54, 83, 710, 3284, 22712, 45139, 37148, 20690, 1900, 15, 83, 124, 1460, 8331, 76145

Offset

1,1

Comments

Table starts

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

..3..5....10.....21.......45.........88.........181.........378.........710

..4..2....22.....74......158........448........1272........3284........8331

..7..3....97....515.....1563.......5915.......22712.......76145......270960

.10..5...213...1527.....7495......45139......282527.....1304136.....6927135

.15..6...381...5304....37148.....377314.....4122537....29425635...269064197

.24..9..1005..20690...218885....4136727....79901137..1058201862.16609740868

.35.10..1900..61348..1059975...34541924..1231102996.34796682706

.54.15..4137.257119..7257895..418453966.26880310825

.83.21.10518.920918.44141371.4088141292

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 11] for n>13

Empirical for row n:

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

n=2: [order 22] for n>24

Example

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

Crossrefs

Column and row 1 are A159288(n+1)

Sequence in context: A357431 A361383 A240153 * A349320 A078338 A338587

Adjacent sequences: A241432 A241433 A241434 * A241436 A241437 A241438

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 22 2014

Status

approved