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A187163
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Number of 2-step self-avoiding walks on an n X n X n cube summed over all starting positions.
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2
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0, 24, 108, 288, 600, 1080, 1764, 2688, 3888, 5400, 7260, 9504, 12168, 15288, 18900, 23040, 27744, 33048, 38988, 45600, 52920, 60984, 69828, 79488, 90000, 101400, 113724, 127008, 141288, 156600, 172980, 190464, 209088, 228888, 249900, 272160
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OFFSET
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1,2
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COMMENTS
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Row 2 of A187162.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..50
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n) = 6*n^3 - 6*n^2.
From Colin Barker, Apr 20 2018: (Start)
G.f.: 12*x^2*(2 + x) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
a(n) = 12 * A006002(n-1). - Alois P. Heinz, Feb 28 2022
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EXAMPLE
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A solution for 2 X 2 X 2:
0 0 0 0
1 0 2 0
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CROSSREFS
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Cf. A006002, A187162.
Sequence in context: A305950 A060334 A271915 * A211577 A101862 A211591
Adjacent sequences: A187160 A187161 A187162 * A187164 A187165 A187166
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KEYWORD
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nonn,easy
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AUTHOR
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R. H. Hardin, Mar 06 2011
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STATUS
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approved
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