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A202807
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Number of n X 3 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.
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1
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1, 6, 32, 121, 356, 881, 1925, 3830, 7083, 12352, 20526, 32759, 50518, 75635, 110363, 157436, 220133, 302346, 408652, 544389, 715736, 929797, 1194689, 1519634, 1915055, 2392676, 2965626, 3648547, 4457706, 5411111, 6528631, 7832120, 9345545
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = (1/180)*n^6 + (1/20)*n^5 + (13/72)*n^4 - (67/360)*n^2 + (19/20)*n.
G.f.: x*(1 - x + 11*x^2 - 12*x^3 + 6*x^4 - x^5) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
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EXAMPLE
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Some solutions for n=5:
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 1 0 0 1 0 0 0 0 1 2 0 1 1 0 0 0
0 1 2 0 0 1 0 0 1 0 0 0 0 1 2 0 1 1 0 0 2
0 2 2 0 2 3 0 1 3 0 0 2 0 2 2 0 2 2 0 1 2
0 2 4 0 2 3 0 2 4 0 1 3 0 2 2 0 2 2 0 2 2
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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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