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

Author

R. H. Hardin, Mar 28 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

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