A229445 T(n,k)=Number of nXk 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing

3, 4, 5, 5, 7, 8, 6, 10, 13, 12, 7, 14, 22, 25, 17, 8, 19, 37, 53, 47, 23, 9, 25, 60, 109, 128, 84, 30, 10, 32, 93, 212, 324, 293, 142, 38, 11, 40, 138, 387, 753, 915, 625, 228, 47, 12, 49, 197, 665, 1609, 2546, 2402, 1244, 350, 57, 13, 59, 272, 1083, 3184, 6374, 8024

Offset

1,1

Comments

Table starts

..3...4....5....6.....7.....8......9.....10......11......12......13.......14

..5...7...10...14....19....25.....32.....40......49......59......70.......82

..8..13...22...37....60....93....138....197.....272.....365.....478......613

.12..25...53..109...212...387....665...1083....1684....2517....3637.....5105

.17..47..128..324...753..1609...3184...5890...10281...17075...27176....41696

.23..84..293..915..2546..6374..14536..30571...59969..110816..194535...326723

.30.142..625.2402..8024.23610..62205.149031..329106..677706.1314145..2419348

.38.228.1244.5843.23428.81177.247607.676983.1685570.3873314.8307126.16784531

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Formula

Empirical for column k:

k=1: a(n) = (1/2)*n^2 + (1/2)*n + 2

k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 - (1/24)*n^2 + (23/12)*n + 2

k=3: [polynomial of degree 6]

k=4: [polynomial of degree 8]

k=5: [polynomial of degree 10]

k=6: [polynomial of degree 12]

k=7: [polynomial of degree 14]

Empirical for row n:

n=1: a(n) = n + 2

n=2: a(n) = (1/2)*n^2 + (1/2)*n + 4

n=3: a(n) = (1/3)*n^3 + (8/3)*n + 5

n=4: a(n) = (1/4)*n^4 - (1/3)*n^3 + (13/4)*n^2 + (11/6)*n + 7

n=5: a(n) = (11/60)*n^5 - (1/2)*n^4 + (15/4)*n^3 - n^2 + (257/30)*n + 6

n=6: [polynomial of degree 6]

n=7: [polynomial of degree 7]

Example

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

Crossrefs

Column 1 is A022856(n+4)

Row 2 is A145018(n+1)

Sequence in context: A332065 A082514 A227215 * A323743 A261017 A024357

Adjacent sequences: A229442 A229443 A229444 * A229446 A229447 A229448

Keyword

nonn,tabl

Author

R. H. Hardin Sep 23 2013

Status

approved