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A270145
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Number of n X 2 0..7 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling seven exactly once.
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1
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8, 1440, 85056, 4126368, 182257536, 7623445344, 307704553920, 12111206870304, 467855602824192, 17813625850002144, 670485480935347776, 25000461221001205920, 924950147066819934336, 33996076829066361534048
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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) = 66*a(n-1) - 1021*a(n-2) - 2244*a(n-3) - 1156*a(n-4) for n>5.
Conjectures from Colin Barker, Jan 30 2019: (Start)
G.f.: 8*x*(1 - x)^2*(1 + 116*x + 4*x^2) / ((1 + x)^2*(1 - 34*x)^2).
a(n) = (48*(-383214*(-1)^n - 2660911*34^n + 35*(363562*(-1)^n + 115797*34^n)*n)) / 210644875 for n>1.
(End)
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EXAMPLE
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Some solutions for n=3:
..5..0. .3..3. .7..3. .2..2. .2..3. .5..7. .6..5. .5..3. .3..6. .6..3
..1..0. .0..7. .6..5. .4..3. .1..0. .4..3. .6..6. .4..1. .2..1. .4..0
..6..5. .1..1. .2..6. .7..6. .4..6. .7..5. .3..4. .5..5. .3..1. .0..2
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CROSSREFS
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Column 2 of A270150.
Sequence in context: A064073 A282889 A225068 * A201492 A172938 A252176
Adjacent sequences: A270142 A270143 A270144 * A270146 A270147 A270148
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Mar 12 2016
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STATUS
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approved
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