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

0,12

Links

Table of n, a(n) for n=0..85.

Example

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;

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 *)

Prog

(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=', ')

Crossrefs

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

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

Sequence in context: A162246 A277447 A333698 * A118400 A159853 A087698

Adjacent sequences: A213123 A213124 A213125 * A213127 A213128 A213129

Keyword

nonn,tabl

Author

Alex Ratushnyak, Jun 06 2012

Extensions

Offset corrected by Joerg Arndt, Dec 05 2016

Status

approved