A048151 Triangular array T read by rows: T(n,k)=k mod n, for k=1,2,...,n, n=1,2,...

0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0

Offset

1,5

Links

Table of n, a(n) for n=1..91.

Formula

G.f.: x^2*y/((1 - x)*(1 - x*y)^2). - Stefano Spezia, Feb 21 2024

Example

Triangle begins:
  0;
  1, 0;
  1, 2, 0;
  1, 2, 3, 0;
  1, 2, 3, 4, 0;
  ...

Mathematica

Flatten[Table[Mod[k, n], {n, 15}, {k, n}]] (* Harvey P. Dale, Mar 21 2012 *)

Prog

(Python)
from math import isqrt, comb
def A048151(n): return n-comb((m:=isqrt(k:=n+1<<1))+(k>m*(m+1)), 2) # Chai Wah Wu, Apr 09 2025

Crossrefs

As a sequence, essentially same as A002262.

Sequence in context: A025690 A025668 A373748 * A025675 A025682 A025691

Adjacent sequences: A048148 A048149 A048150 * A048152 A048153 A048154

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved