A332749 a(n) is the sum of the residues of the first k positive triangular numbers modulo n, where k = n if n is odd, 2n if n is even.

0, 2, 1, 12, 5, 22, 14, 56, 21, 70, 44, 116, 52, 154, 65, 240, 102, 246, 133, 340, 133, 418, 230, 520, 225, 546, 252, 700, 348, 710, 403, 992, 374, 986, 455, 1140, 555, 1254, 598, 1480, 697, 1414, 774, 1804, 690, 1978, 987, 2192, 980, 2150, 1037, 2444, 1219, 2466

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Example

For n=4 the first 8 positive triangular numbers are {1,3,6,10,15,21,28,36} == {1,3,2,2,3,1,0,0} (mod 4); the sum of the residues is 12, so a(4)=12.
For n=5 the first 5 positive triangular numbers are {1,3,6,10,15} == {1,3,1,0,0} (mod 5); the sum of the residues is 5, so a(5)=5.

Mathematica

Riffle[Table[
  Total[Table[
    Mod[Table[(n (n + 1)/2), {n, 1, (2 y - 1)}], (2 y - 1)]]], {y, 1,
   t}] , Table[
  Total[Table[Mod[Table[(n (n + 1)/2), {n, 1, (4 l)}], (2 l)]]], {l,
   1, t}]]

Crossrefs

Sequence in context: A357013 A370552 A167128 * A342430 A181417 A048743

Adjacent sequences: A332746 A332747 A332748 * A332750 A332751 A332752

Keyword

nonn

Author

Tolga Kurt, Feb 22 2020

Status

approved