A027300 Triangular array Q given by rows: Q(n,k) = number of partitions of n that do not contain k as an element; domain: 1 <= k <= n, n >= 1.

0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 2, 4, 5, 6, 6, 4, 6, 8, 9, 10, 10, 4, 8, 10, 12, 13, 14, 14, 7, 11, 15, 17, 19, 20, 21, 21, 8, 15, 19, 23, 25, 27, 28, 29, 29, 12, 20, 27, 31, 35, 37, 39, 40, 41, 41, 14, 26, 34, 41, 45, 49, 51, 53, 54, 55, 55, 21, 35

Offset

1,5

Links

Table of n, a(n) for n=1..68.

Formula

Q(n, k) = P(n+1, 1) - P(n, k), P given by A027293.

Q(n, k) = A000041(n) - A000041(n - k). - Sean A. Irvine, Oct 26 2019

Example

Triangle begins:
  0,
  1, 1,
  1, 2, 2,
  2, 3, 4, 4,
  2, 4, 5, 6, 6,
  ...

Crossrefs

Cf. A000041, A027293.

Sequence in context: A071454 A178139 A039642 * A085313 A065458 A341121

Adjacent sequences: A027297 A027298 A027299 * A027301 A027302 A027303

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved