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

Author

R. H. Hardin Sep 23 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A022856(n+4)

Row 2 is A145018(n+1)

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]