login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 27 05:27 EST 2020. Contains 338678 sequences. (Running on oeis4.)