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A186096
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T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order
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10
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102251, 1252889, 1252889, 11258613, 22559052, 11258613, 83378583, 280102672, 280102672, 83378583, 531218757, 2743553694, 4527262140, 2743553694, 531218757, 2985984444, 22408644868, 55707179395, 55707179395, 22408644868, 2985984444
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OFFSET
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1,1
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COMMENTS
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Table starts
........102251.........1252889.........11258613...........83378583
.......1252889........22559052........280102672.........2743553694
......11258613.......280102672.......4527262140........55707179395
......83378583......2743553694......55707179395.......837192826927
.....531218757.....22408644868.....558643720724.....10064164793382
....2985984444....157927508610....4754203179765....101247852066065
...15084070635....983600385660...35285910378578....878623899164100
...69482992431...5510351270895..232998389350277...6723402580436327
..295278398390..28148281162513.1389861134920751..46135247077059665
.1168636004931.132536596243411.7581135805604097.287649593317228144
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..219
R. H. Hardin, Polynomials for columns 1-8
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FORMULA
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Empirical: T(n,k) is a polynomial of degree 4k+30 in n, for fixed k.
Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.
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EXAMPLE
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Some solutions for 5X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..2....0..0..0..2....0..0..0..2....0..0..1..2....0..0..1..2
..0..1..2..1....1..1..2..2....1..1..2..0....1..2..4..4....0..2..1..2
..2..3..3..4....1..2..0..0....3..4..0..1....1..4..1..3....2..4..3..2
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CROSSREFS
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Sequence in context: A153050 A203592 A106813 * A186088 A186087 A106814
Adjacent sequences: A186093 A186094 A186095 * A186097 A186098 A186099
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Feb 12 2011
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STATUS
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approved
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