A240433 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4

2, 2, 2, 4, 6, 4, 4, 24, 24, 4, 8, 58, 206, 58, 8, 8, 236, 970, 970, 236, 8, 16, 566, 8084, 9036, 8084, 566, 16, 16, 2322, 38406, 150350, 150350, 38406, 2322, 16, 32, 5578, 319164, 1404008, 5087802, 1404008, 319164, 5578, 32, 32, 22912, 1514122, 23414762

Offset

1,1

Comments

Table starts

..2.....2........4...........4..............8...............8...............16

..2.....6.......24..........58............236.............566.............2322

..4....24......206.........970...........8084...........38406...........319164

..4....58......970........9036.........150350.........1404008.........23414762

..8...236.....8084......150350........5087802........94860720.......3184383016

..8...566....38406.....1404008.......94860720......3523795084.....237034323164

.16..2322...319164....23414762.....3184383016....237034323164...32020507274002

.16..5578..1514122...218412550....59125702284...8779074387924.2372829502697230

.32.22912.12567490..3639548326..1979684295626.589446737374098

.32.55054.59600672.33928317272.36705060609854

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-2)

k=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)

k=3: [order 48]

Example

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

Crossrefs

Column 1 is A016116(n+1)

Sequence in context: A152968 A222177 A342271 * A217637 A231515 A231544

Adjacent sequences: A240430 A240431 A240432 * A240434 A240435 A240436

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 04 2014

Status

approved