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A090026
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Number of distinct lines through the origin in 4-dimensional cube of side length n.
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12
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0, 15, 65, 225, 529, 1185, 2065, 3745, 5841, 9105, 13025, 19105, 25521, 35361, 45825, 59905, 75425, 96865, 117841, 147505, 177041, 214961, 254401, 306321, 355249, 420929, 485489, 565265, 645377, 748081, 841841, 966881, 1086241, 1230401
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Equivalently, lattice points where the GCD of all coordinates = 1.
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FORMULA
| a(n) = A090030(4, n)
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EXAMPLE
| a(2) = 65 because the 65 points with at least one coordinate=2 all make distinct lines and the remaining 15 points and the origin are on those lines.
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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}]]; lines[n_, k_] := (k + 1)^n - Sum[Floor[k/i - 1]*aux[n, i], {i, 1, Floor[k/2]}] - 1; Table[lines[4, k], {k, 0, 40}]
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CROSSREFS
| Cf. A000225, A001047, A060867, A090020, A090021, A090022, A090023, A090024 are for n dimensions with side length 1, 2, 3, 4, 5, 6, 7, 8, respectively. A049691, A090025, A090026, A090027, A090028, A090029 are this sequence for 2, 3, 4, 5, 6, 7 dimensions. A090030 is the table for n dimensions, side length k.
Sequence in context: A027455 A152729 A055268 * A027526 A033653 A088058
Adjacent sequences: A090023 A090024 A090025 * A090027 A090028 A090029
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KEYWORD
| nonn
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AUTHOR
| Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Nov 25 2003
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