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A212031
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Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element at a city block distance of two, and containing the value n(n+1)/2-2.
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1
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0, 3, 10, 31, 78, 166, 313, 540, 871, 1333, 1956, 2773, 3820, 5136, 6763, 8746, 11133, 13975, 17326, 21243, 25786, 31018, 37005, 43816, 51523, 60201, 69928, 80785, 92856, 106228, 120991, 137238, 155065, 174571, 195858, 219031, 244198, 271470, 300961
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OFFSET
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1,2
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COMMENTS
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Column 1 of A212036.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..70
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FORMULA
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Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (17/8)*n^2 + (19/4)*n - 2 for n>1.
Conjectures from Colin Barker, Jul 20 2018: (Start)
G.f.: x^2*(3 - 5*x + 11*x^2 - 7*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
(End)
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EXAMPLE
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Some solutions for n=4:
..0........0........0........0........0........0........0........0
..1.2......1.2......1.2......1.2......1.2......1.1......1.2......1.2
..1.3.4....3.2.4....3.4.5....3.4.5....3.0.4....2.3.4....3.4.5....3.4.1
..5.6.7.8..5.6.7.8..6.7.3.8..6.7.8.6..5.6.7.8..5.6.7.8..5.6.7.8..5.6.7.8
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CROSSREFS
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Cf. A212036.
Sequence in context: A316764 A331780 A290061 * A339032 A033121 A180432
Adjacent sequences: A212028 A212029 A212030 * A212032 A212033 A212034
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Apr 27 2012
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STATUS
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approved
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