A240000 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4

2, 3, 5, 4, 13, 12, 5, 25, 61, 28, 6, 42, 190, 256, 66, 7, 65, 526, 1372, 1117, 156, 8, 95, 1262, 6527, 10405, 5012, 368, 9, 133, 2766, 27415, 86360, 83029, 22592, 868, 10, 180, 5647, 104291, 635873, 1225281, 685898, 102336, 2048, 11, 237, 10878, 363859

Offset

1,1

Comments

Table starts

....2.......3.........4...........5............6............7............8

....5......13........25..........42...........65...........95..........133

...12......61.......190.........526.........1262.........2766.........5647

...28.....256......1372........6527........27415.......104291.......363859

...66....1117.....10405.......86360.......635873......4267171.....26152051

..156....5012.....83029.....1225281.....15981219....191691132...2090236137

..368...22592....685898....18392485....429788876...9314138750.182333502325

..868..102336...5825700...290513038..12392346376.491124025940

.2048..465662..50417154..4767970186.378942837634

.4832.2123857.441675344.80410934960

Links

R. H. Hardin, Table of n, a(n) for n = 1..98

Formula

Empirical for column k:

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

k=2: [order 26]

Empirical for row n:

n=1: a(n) = n + 1

n=2: a(n) = (1/6)*n^3 + 1*n^2 + (23/6)*n

n=3: [polynomial of degree 8] for n>6

n=4: [polynomial of degree 19] for n>20

n=5: [polynomial of degree 44] for n>52

Example

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

Crossrefs

Column 1 is A239333

Sequence in context: A131401 A061446 A280690 * A193770 A107476 A094140

Adjacent sequences: A239997 A239998 A239999 * A240001 A240002 A240003

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 30 2014

Status

approved