login
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
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
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
KEYWORD
nonn
AUTHOR
Tolga Kurt, Feb 22 2020
STATUS
approved