A167271 Triangle read by rows: T(n,k) = A167269(n/k-1, k-1) if k divides n, T(n,k) = 0 otherwise.

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

Offset

1,8

Comments

To form column k+1, aerate the terms of column k of A167269 with k zeros.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275

Example

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

Prog

(PARI) T(n, k) = if(n%k==0, if(k%2, 1, binomial(n/k + k/2 - 1, k/2))) \\ Andrew Howroyd, Sep 20 2025

Crossrefs

Row sums are A167272.

Infinite product of shifted columns gives A167273.

Cf. A167269.

Sequence in context: A286563 A216282 A147861 * A156348 A306437 A343746

Adjacent sequences: A167268 A167269 A167270 * A167272 A167273 A167274

Keyword

nonn,tabl

Author

Gary W. Adamson & Mats Granvik, Oct 31 2009

Extensions

Name edited and offset changed by Andrew Howroyd, Sep 20 2025

Status

approved