A213126 Rows of triangle formed using Pascal's rule, except sums in the n-th row are modulo n: T(n,0) = T(n,n) = 1 and T(n,k) = (T(n-1,k-1) + T(n-1,k)) mod n.

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

Offset: 0

Author

Alex Ratushnyak, Jun 06 2012

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1;
  1,  1;
  1,  0,  1;
  1,  1,  1,  1;
  1,  2,  2,  2,  1;
  1,  3,  4,  4,  3,  1;
  1,  4,  1,  2,  1,  4,  1;
  1,  5,  5,  3,  3,  5,  5,  1;
  1,  6,  2,  0,  6,  0,  2,  6,  1;
  1,  7,  8,  2,  6,  6,  2,  8,  7,  1;
  1,  8,  5,  0,  8,  2,  8,  0,  5,  8,  1;
  1,  9,  2,  5,  8, 10, 10,  8,  5,  2,  9,  1;
		

Crossrefs

Cf. A007318 - Pascal's triangle read by rows.

Cf. A047999, A083093, A034931, A034930, A034932, A008975.

Programs

Mathematica

T[n_,k_]:=If[k==0 || k==n, 1, Mod[T[n - 1, k - 1] + T[n- 1, k], n]]; Table[T[n, k], {n, 0, 15}, {k, 0, n}] // Flatten (* Indranil Ghosh, Apr 29 2017 *)

Python

src = [0]*1024
dst = [0]*1024
for n in range(19):
    dst[0] = dst[n] = 1
    for k in range(1, n):
        dst[k] = (src[k-1]+src[k]) % n
    for k in range(n+1):
        src[k] = dst[k]
        print(dst[k], end=',')

Extensions

Offset corrected by Joerg Arndt, Dec 05 2016