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A229442
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Number of n X 5 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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1
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7, 19, 60, 212, 753, 2546, 8024, 23428, 63430, 159945, 377840, 841419, 1777036, 3578998, 6908102, 12834739, 23041529, 40103959, 67871516, 111976374, 180501843, 284848554, 440842772, 670138334, 1001971536, 1475336877, 2141660944
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OFFSET
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1,1
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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Empirical: a(n) = (1/103680)*n^10 + (1/80640)*n^9 + (1/12096)*n^8 + (47/13440)*n^7 + (11/6912)*n^6 + (173/3840)*n^5 + (1187/10368)*n^4 + (12437/20160)*n^3 - (6211/10080)*n^2 + (4901/840)*n + 1.
Conjectures from Colin Barker, Sep 17 2018: (Start)
G.f.: x*(7 - 58*x + 236*x^2 - 558*x^3 + 896*x^4 - 941*x^5 + 709*x^6 - 343*x^7 + 103*x^8 - 17*x^9 + x^10) / (1 - x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
(End)
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EXAMPLE
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Some solutions for n=4:
..0..0..0..0..2....0..2..2..2..2....0..0..2..2..2....0..2..2..2..2
..0..0..0..0..2....1..0..2..2..2....1..1..0..2..2....1..0..2..2..2
..1..1..1..1..0....1..1..0..2..2....1..1..1..0..0....1..1..0..0..0
..1..1..1..1..1....1..1..0..2..2....1..1..1..1..1....1..1..1..1..1
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CROSSREFS
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Column 5 of A229445.
Sequence in context: A263335 A155335 A155226 * A179406 A165683 A092359
Adjacent sequences: A229439 A229440 A229441 * A229443 A229444 A229445
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KEYWORD
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nonn
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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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