A241397 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 zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4

2, 2, 3, 4, 5, 4, 6, 9, 13, 7, 8, 23, 29, 28, 10, 14, 44, 85, 97, 64, 15, 20, 93, 201, 480, 340, 142, 24, 30, 204, 689, 1657, 2780, 1156, 318, 35, 48, 368, 1929, 8697, 15339, 17211, 4068, 726, 54, 70, 761, 4068, 31654, 129985, 160947, 102782, 14763, 1634, 83, 108

Offset

1,1

Comments

Table starts

..2....2......4........6..........8..........14..........20.........30

..3....5......9.......23.........44..........93.........204........368

..4...13.....29.......85........201.........689........1929.......4068

..7...28.....97......480.......1657........8697.......31654......92204

.10...64....340.....2780......15339......129985......667050....2949778

.15..142...1156....17211.....160947.....2234804....18589398..134190457

.24..318...4068...102782....1622867....39781828...541660724.7518340973

.35..726..14763...645484...18627122...821631365.21331876978

.54.1634..52950..3936420..196990531.16108803423

.83.3695.190950.24633252.2356216195

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 38]

Empirical for row n:

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

n=2: [order 22] for n>23

Example

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

Crossrefs

Column 1 is A159288(n+1)

Row 1 is A239851

Sequence in context: A275495 A022820 A292259 * A331049 A350127 A320159

Adjacent sequences: A241394 A241395 A241396 * A241398 A241399 A241400

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 20 2014

Status

approved