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

Author

R. H. Hardin, Apr 20 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A159288(n+1).

Column 2 is A226503(n+8).

Row 1 is A239851.

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.