A240412 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero 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, modulo 4

2, 2, 5, 4, 10, 11, 6, 32, 33, 25, 8, 80, 202, 139, 57, 14, 162, 846, 1526, 529, 129, 20, 493, 3035, 11670, 10749, 2105, 293, 30, 1109, 17075, 74655, 148536, 79090, 8258, 665, 48, 2656, 65790, 773196, 1765436, 2051450, 573490, 32480, 1509, 70, 7235, 283052

Offset

1,1

Comments

Table starts

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

....5.....10........32..........80..........162...........493..........1109

...11.....33.......202.........846.........3035.........17075.........65790

...25....139......1526.......11670........74655........773196.......5429095

...57....529.....10749......148536......1765436......33373526.....425530595

..129...2105.....79090.....2051450.....45245148....1615637679...38249442962

..293...8258....573490....27295809...1123774316...74389514201.3275332362582

..665..32480...4185321...377924479..29595088887.3790596926634

.1509.127944..30488162..5090700587.749274246946

.3425.503372.222232658.70407569019

Links

R. H. Hardin, Table of n, a(n) for n = 1..98

Formula

Empirical for column k:

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

k=2: [order 14]

Empirical for row n:

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

n=2: [order 15] for n>16

Example

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

Crossrefs

Column 1 is A239812

Row 1 is A239851

Sequence in context: A056444 A319925 A112472 * A292263 A338528 A238624

Adjacent sequences: A240409 A240410 A240411 * A240413 A240414 A240415

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 04 2014

Status

approved