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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
12
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
1,1
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
LINKS
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
EXAMPLE
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
CROSSREFS
Column 1 is A239812
Row 1 is A239851
Sequence in context: A284127 A261114 A284827 * A336073 A266792 A162200
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 18 2014
STATUS
approved