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Search: id:A081474
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| A081474 |
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Number of distinct lines through the origin in n-dimensional cube of side length n. |
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+0
1
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| 0, 1, 5, 49, 529, 7471, 112825, 2078455, 42649281, 997784221, 25875851825, 742641202183, 23283999690561, 793616663524231, 29188521870580929, 1152885848976064513, 48659336030073207425, 2185894865613157551481
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OFFSET
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0,3
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COMMENT
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Equivalently, lattice points where the GCD of all coordinates = 1.
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FORMULA
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a(n) = A090030(n, n)
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EXAMPLE
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a(3) = 49 because in the 3-dimensional lattice of side length 3, the lines through the origin are determined by all 37 points with at least one coordinate = 3 and 6 permutations of (2,1,0) and 3 permutations each of (2,1,1) and (2,2,1).
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MATHEMATICA
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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[k, k], {k, 0, 20}]
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CROSSREFS
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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: A096596 A146311 A001079 this_sequence A112241 A116873 A089914
Adjacent sequences: A081471 A081472 A081473 this_sequence A081475 A081476 A081477
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KEYWORD
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nonn
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AUTHOR
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Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Nov 25 2003
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