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A229424
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Number of n X 4 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
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2
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12, 55, 222, 754, 2204, 5700, 13345, 28794, 58053, 110550, 200533, 348855, 585211, 950897, 1502166, 2314261, 3486210, 5146473, 7459536, 10633552, 14929134, 20669410, 28251455, 38159220, 50978083, 67411152, 88297455, 114632157
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = (1/8064)*n^8 + (1/288)*n^7 + (103/2880)*n^6 + (17/90)*n^5 + (751/1152)*n^4 + (571/288)*n^3 + (7769/3360)*n^2 + (153/40)*n + 3.
G.f.: x*(12 - 53*x + 159*x^2 - 272*x^3 + 302*x^4 - 222*x^5 + 103*x^6 - 27*x^7 + 3*x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)
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EXAMPLE
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Some solutions for n=4:
..2..2..1..0....1..1..0..0....2..1..0..0....1..1..1..0....1..0..0..0
..2..2..2..1....2..1..0..0....2..2..1..1....2..1..1..0....2..1..0..0
..2..2..2..1....2..1..1..1....2..2..1..1....2..2..1..0....2..1..1..1
..2..2..2..1....2..2..2..2....2..2..2..2....2..2..2..1....2..1..1..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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