A239858 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 one 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, 3, 4, 6, 9, 5, 6, 8, 12, 44, 4, 8, 14, 29, 78, 84, 5, 14, 20, 63, 255, 203, 130, 5, 20, 30, 100, 742, 1114, 484, 343, 6, 30, 48, 215, 1382, 3463, 4549, 1757, 685, 10, 48, 70, 468, 5647, 9963, 19065, 28184, 4979, 1704, 11, 70, 108, 785, 14755, 71695, 77212

Offset

1,1

Comments

Table starts

..2..2....4......6........8........14.........20..........30.........48

..2..3....9.....12.......29........63........100.........215........468

..4..5...44.....78......255.......742.......1382........5647......14755

..6..4...84....203.....1114......3463.......9963.......71695.....219708

..8..5..130....484.....4549.....19065......77212......970717....4024283

.14..5..343...1757....28184....176208.....937154....23072270..141040759

.20..6..685...4979...125255...1162638....9885999...421824199.5282952362

.30.10.1704..19850...860559..11924924..147826427.14757679494

.48.11.3977..68830..4802971.111900643.2030390429

.70.15.7958.207822.24477675.995175724

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: a(n) = a(n-2) +a(n-5) for n>9

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..3....2..3..3..2....2..3..3..3....3..2..2..2....2..3..2..2
..2..1..1..2....3..1..1..3....3..1..1..2....2..1..0..0....3..1..1..0
..3..0..2..2....3..1..1..2....3..2..2..2....3..1..3..0....2..1..2..0
..3..2..0..0....2..3..0..2....2..3..0..0....2..3..3..3....2..0..0..3

Crossrefs

Sequence in context: A241164 A029157 A247301 * A031437 A282561 A237598

Adjacent sequences: A239855 A239856 A239857 * A239859 A239860 A239861

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 28 2014

Status

approved