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A240192
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 three plus the sum of the elements diagonally to its northwest, modulo 4
12
1, 1, 2, 1, 5, 3, 1, 8, 12, 4, 1, 14, 37, 27, 7, 1, 26, 129, 138, 73, 10, 1, 50, 478, 771, 680, 154, 15, 1, 98, 1908, 5240, 7170, 2413, 358, 24, 1, 194, 7868, 40765, 91879, 44594, 10017, 872, 35, 1, 386, 32888, 336257, 1399773, 1005029, 333607, 43956, 1871, 54, 1
OFFSET
1,3
COMMENTS
Table starts
..1....1......1.........1...........1............1.............1.............1
..2....5......8........14..........26...........50............98...........194
..3...12.....37.......129.........478.........1908..........7868.........32888
..4...27....138.......771........5240........40765........336257.......2843914
..7...73....680......7170.......91879......1399773......22849697.....385366572
.10..154...2413.....44594.....1005029.....28061567.....865984451...28244997476
.15..358..10017....333607....14022582....733907809...43398047802.2752449791995
.24..872..43956...2715035...206345434..19388521135.2070573220929
.35.1871.159668..17332017..2336659626.394134037392
.54.4438.681760.134735700.33576330306
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-2) +2*a(n-3)
k=2: [order 13]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 3*a(n-1) -2*a(n-2) for n>3
n=3: a(n) = 9*a(n-1) -27*a(n-2) +29*a(n-3) +6*a(n-4) -32*a(n-5) +16*a(n-6) for n>9
n=4: [order 29] for n>34
EXAMPLE
Some solutions for n=4 k=4
..2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0
..1..2..0..0....2..3..0..2....2..0..0..0....2..0..0..0....2..0..0..0
..2..1..0..2....2..3..3..1....2..0..3..0....2..3..0..2....2..0..3..2
..1..3..2..0....1..2..1..1....2..0..3..3....1..2..2..0....1..0..2..1
CROSSREFS
Column 1 is A159288
Row 2 is A164094(n-2)
Sequence in context: A329440 A339494 A104731 * A264751 A209130 A330381
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 02 2014
STATUS
approved