A241356 T(n,k) = Number of n X k 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 or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

2, 2, 3, 4, 3, 4, 6, 9, 3, 7, 8, 17, 19, 4, 10, 14, 23, 51, 55, 5, 15, 20, 53, 61, 128, 72, 5, 24, 30, 103, 230, 228, 248, 124, 7, 35, 48, 160, 641, 1721, 615, 624, 243, 8, 54, 70, 344, 960, 5663, 6307, 2062, 1323, 370, 9, 83, 108, 643, 3746, 11909, 32942, 35880, 6380, 2715

Offset

1,1

Comments

Table starts

..2..2...4.....6......8.......14........20.........30.........48.........70

..3..3...9....17.....23.......53.......103........160........344........643

..4..3..19....51.....61......230.......641........960.......3746.......9339

..7..4..55...128....228.....1721......5663......11909......69946.....220363

.10..5..72...248....615.....6307.....32942......81541.....704210....3476469

.15..5.124...624...2062....35880....247664.....921726...10840453...85630246

.24..7.243..1323...6380...183400...1904754...10693549..198803445.2384535274

.35..8.370..2715..17325...763750..12340892..109041097.3042023002

.54..9.695..5798..60671..4110488.104529676.1490516896

.83.12.956.11469.174659.18352240.729080777

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

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

k=2: a(n) = a(n-3) +a(n-5).

k=3: [order 68] for n > 85.

Empirical for row n:

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

n=2: [order 17] for n > 20.

Example

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

Crossrefs

Column 1 is A159288(n+1).

Column 2 is A226503(n+8).

Row 1 is A239851.

Sequence in context: A003991 A131923 A119457 * A065157 A235804 A051597

Adjacent sequences: A241353 A241354 A241355 * A241357 A241358 A241359

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 20 2014

Status

approved