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A229445
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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
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13
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..480
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FORMULA
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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]
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EXAMPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin Sep 23 2013
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STATUS
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approved
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