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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
13
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Sep 23 2013
STATUS
approved