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A090225
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T(n,k) = Points in n-dimensional lattice of side length k with at least one coordinate = k and GCD of all coordinates = 1.
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1
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0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 2, 7, 0, 0, 0, 4, 12, 15, 0, 0, 0, 4, 30, 50, 31, 0, 0, 0, 8, 42, 160, 180, 63, 0, 0, 0, 4, 84, 304, 750, 602, 127, 0, 0, 0, 12, 78, 656, 1890, 3304, 1932, 255, 0, 0, 0, 8, 162, 880, 4620, 10864, 14070, 6050, 511, 0, 0, 0, 12, 156, 1680, 8070
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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FORMULA
| T(n, 0) = 0; T(n, k) = (k+1)^n - k^n - sum T(n, divisors of k)
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EXAMPLE
| T(3,2) = 12 because of the six permutations of (2,1,0) and three each of (2,1,1) and (2,2,1).
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MATHEMATICA
| aux[n_, k_] := If[k == 0, 0, (k + 1)^n - k^n - Sum[aux[n, Divisors[k][[i]]], {i, 1, Length[Divisors[k]] - 1}]]
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CROSSREFS
| Cf. A090030.
Sequence in context: A036873 A081130 A174428 * A206705 A200221 A158678
Adjacent sequences: A090222 A090223 A090224 * A090226 A090227 A090228
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KEYWORD
| nonn,tabl
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AUTHOR
| Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Nov 24 2003
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