A240271 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 one plus the sum of the elements diagonally to its northwest, modulo 4

2, 4, 3, 10, 7, 4, 24, 35, 14, 7, 56, 157, 118, 36, 10, 132, 713, 919, 582, 72, 15, 312, 3263, 7562, 8265, 2000, 170, 24, 736, 14895, 64721, 126286, 49921, 8353, 411, 35, 1736, 68101, 563496, 2059061, 1363144, 382690, 37422, 879, 54, 4096, 311509, 4956889

Offset

1,1

Comments

Table starts

..2....4......10.........24..........56..........132...........312

..3....7......35........157.........713.........3263.........14895

..4...14.....118........919........7562........64721........563496

..7...36.....582.......8265......126286......2059061......34514871

.10...72....2000......49921.....1363144.....40760821....1277623744

.15..170....8353.....382690....19210586...1063706501...63085436203

.24..411...37422....3076452...278945445..27923918285.3004792552569

.35..879..135463...19781372..3200032085.576407548906

.54.2106..580528..154994425.46095401280

.83.4874.2403439.1144262410

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

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

n=2: [order 26] for n>28

Example

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

Crossrefs

Column 1 is A159288(n+1)

Row 1 is A052912

Sequence in context: A183210 A226367 A324934 * A208324 A277416 A064691

Adjacent sequences: A240268 A240269 A240270 * A240272 A240273 A240274

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 03 2014

Status

approved