A049318 Number of 3-dimensional integer direction vectors (a,b,c) towards grid points at squared integer distance 2n-1 with a >= 0, b >= 0, c >= 0.

3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 24, 18, 18, 27, 24, 24, 36, 24, 30, 36, 33, 33, 36, 36, 42, 48, 42, 36, 60, 45, 48, 72, 42, 51, 72, 54, 57, 60, 72, 60, 81, 63, 54, 84, 69, 72, 96, 60, 75, 108, 78, 78, 96, 81, 84, 108, 87, 72, 108, 96, 99, 120, 78, 96, 132, 99, 120

Offset

1,1

Comments

A vector is a direction vector if its nonzero components have their GCD = 1.

Links

Table of n, a(n) for n=1..67.

Example

The 4 directions towards points at squared distance 29 (i.e. for n=15) are (signed permutations of) [ 24,16,3 ],[ 24,12,11 ],[ 21,20,0 ],[ 21,16,12 ]

Crossrefs

Cf. A049317, A049319.

Sequence in context: A110261 A168237 A290966 * A325861 A376449 A079551

Adjacent sequences: A049315 A049316 A049317 * A049319 A049320 A049321

Keyword

nonn

Author

Wouter Meeussen

Extensions

Missing a(52)=78 inserted by Sean A. Irvine, Jul 28 2021

Status

approved