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

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

R. H. Hardin, Table of n, a(n) for n = 1..112

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

Adjacent sequences: A240189 A240190 A240191 * A240193 A240194 A240195

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 02 2014

Status

approved