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A090026 Number of distinct lines through the origin in 4-dimensional cube of side length n. 12
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; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..33.

FORMULA

a(n) = A090030(4, n)

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.

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}]

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 A284898 A033653

Adjacent sequences:  A090023 A090024 A090025 * A090027 A090028 A090029

KEYWORD

nonn

AUTHOR

Joshua Zucker, Nov 25 2003

STATUS

approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)