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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A090027 Number of distinct lines through the origin in 5-dimensional cube of side length n. 12
 0, 31, 211, 961, 2851, 7471, 15541, 31471, 55651, 95821, 152041, 239791, 351331, 517831, 723241, 1007041, 1352041, 1821721, 2359051, 3082921, 3904081, 4956901, 6151651, 7677901, 9334261, 11445361, 13746181, 16566691, 19644031, 23432851, 27408331, 32333581 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equivalently, number of lattice points where the GCD of all coordinates = 1. LINKS FORMULA a(n) = A090030(5, n). a(n) = (n+1)^5 - 1 - Sum_{j=2..n+1} a(floor(n/j)). - Chai Wah Wu, Mar 30 2021 EXAMPLE a(2) = 211 because the 211 points with at least one coordinate=2 all make distinct lines and the remaining 31 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[5, k], {k, 0, 40}] PROG (Python) from functools import lru_cache @lru_cache(maxsize=None) def A090027(n):     if n == 0:         return 0     c, j = 1, 2     k1 = n//j     while k1 > 1:         j2 = n//k1 + 1         c += (j2-j)*A090027(k1)         j, k1 = j2, n//j2     return (n+1)**5-c+31*(j-n-1) # Chai Wah Wu, Mar 30 2021 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: A142328 A022521 A152730 * A164784 A290008 A121616 Adjacent sequences:  A090024 A090025 A090026 * A090028 A090029 A090030 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.

Last modified June 14 13:23 EDT 2021. Contains 345025 sequences. (Running on oeis4.)