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Search: id:A144045
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| A144045 |
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The number of paths of a chess Rook in a cube, from (1,1,1) to (n,n,n), where the rook may move in steps that are multiples of (1,0,0), (0,0,1), or (0,0,1). |
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+0
1
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| 1, 6, 222, 9918, 486924, 25267236, 1359631776, 75059524392, 4223303759148, 241144782230124, 13930829740017132, 812470444305924300, 47760356825349969600, 2826309951801018736800, 168207011284961649886800
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OFFSET
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0,2
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FORMULA
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a(n) satisfies the recurrence relation a(1) = 1; a(2) = 6; a(3) = 222; a(4) = 9918; a(n) = ((-121 n^3 + 575n^2 - 872n + 412)a(n - 1) + (-475n^3 + 4887n^2 - 16202n + 17448)a(n - 2) + (1746n^3 - 19818n^2 + 75060n - 94896)a(n - 3) + (-1152n^3 + 16128n^2 - 74880n + 115200)a(n - 4))/(-(2n^3 - 8n^2 + 10n - 4)), n>= 5.
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EXAMPLE
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a(2)=6 because there are 6 Rook paths from (1,1,1) to (2,2,2).
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CROSSREFS
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Sequence in context: A041623 A015477 A144658 this_sequence A061610 A054324 A117255
Adjacent sequences: A144042 A144043 A144044 this_sequence A144046 A144047 A144048
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KEYWORD
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nonn
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AUTHOR
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Martin J. Erickson (erickson(AT)truman.edu), Sep 08 2008
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