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A081474 Number of distinct lines through the origin in n-dimensional cube of side length n. 0
0, 1, 5, 49, 529, 7471, 112825, 2078455, 42649281, 997784221, 25875851825, 742641202183, 23283999690561, 793616663524231, 29188521870580929, 1152885848976064513, 48659336030073207425, 2185894865613157551481 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equivalently, lattice points where the GCD of all coordinates = 1.

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = A090030(n, n)

EXAMPLE

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).

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[k, k], {k, 0, 20}]

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: A146311 A212818 A195206 * A274671 A112241 A216483

Adjacent sequences:  A081471 A081472 A081473 * A081475 A081476 A081477

KEYWORD

nonn

AUTHOR

Joshua Zucker, Nov 25 2003

STATUS

approved

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.