A241306 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 or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

2, 2, 5, 4, 6, 11, 6, 15, 6, 25, 8, 25, 37, 12, 57, 14, 40, 74, 116, 16, 129, 20, 89, 186, 330, 304, 28, 293, 30, 121, 646, 1462, 1145, 869, 38, 665, 48, 237, 1278, 5757, 6718, 4499, 2398, 66, 1509, 70, 390, 3418, 22343, 49918, 41336, 15827, 6813, 92, 3425, 108, 682

Offset: 1

Author

R. H. Hardin, Apr 18 2014

Keywords

• nonn
• tabl

Comments

Table starts

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

....5...6....15.....25.......40.........89.........121.........237.........390

...11...6....37.....74......186........646........1278........3418........9113

...25..12...116....330.....1462.......5757.......22343.......79043......304799

...57..16...304...1145.....6718......49918......283985.....1666242.....9581018

..129..28...869...4499....41336.....490486.....5098814....41458261...447396605

..293..38..2398..15827...217785....3893262....70316883...978925384.16677156613

..665..66..6813..58043..1215485...37039909..1194164944.30759996872

.1509..92.18782.209838..6526016..307030328.16586413847

.3425.154.53067.757771.35833494.2801405991

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..126

Crossrefs

Column 1 is A239812

Row 1 is A239851

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-2) +a(n-3) -a(n-5)

Empirical for row n:

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

n=2: [order 14] for n>20