

A081474


Number of distinct lines through the origin in ndimensional cube of side length n.


0



0, 1, 5, 49, 529, 7471, 112825, 2078455, 42649281, 997784221, 25875851825, 742641202183, 23283999690561, 793616663524231, 29188521870580929, 1152885848976064513, 48659336030073207425, 2185894865613157551481
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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 3dimensional 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



