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

Author

R. H. Hardin, Apr 02 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A159288

Row 2 is A164094(n-2)

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