A231642 Triangle read by rows, t(n,k) = binomial(n,k) mod n, k <= n.

0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 3, 2, 3, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 6, 0, 4, 0, 1, 0, 0, 3, 0, 0, 3, 0, 0, 1, 0, 5, 0, 0, 2, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 6, 4, 3, 0, 0, 0, 3, 4, 6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 7, 0, 7, 0, 7, 2, 7, 0, 7, 0, 7, 0, 1

Offset

1,8

Comments

Rows of the form 0,0,0,...,0,1 fit prime n.

Links

T. D. Noe, Rows n = 1..100 of triangle, flattened

Frank Ruskey, Carla D. Savage, and Stan Wagon, The Search for Simple Symmetric Venn Diagrams, Notices Amer. Math. Soc. 53 (2006), no. 11, 1304-1311., page 1.

Example

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

Mathematica

t[n_, k_] := Mod[Binomial[n, k], n]; Table[t[n, k], {n, 14}, {k, n}] // Flatten

Prog

(PARI) t(n, k)=binomial(n, k)%n \\ Charles R Greathouse IV, Nov 12 2013

Crossrefs

Sequence in context: A331671 A373925 A123758 * A288318 A354099 A219483

Adjacent sequences: A231639 A231640 A231641 * A231643 A231644 A231645

Keyword

nonn,tabl

Author

Jean-François Alcover, Nov 12 2013

Status

approved