A132825 Triangle read by rows: zeros except for right border which are the partition numbers A000041.

1, 0, 2, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101

Offset

1,3

Comments

Row sums = partition numbers, A000041 starting with A000041(1).

A132825 * [1, 2, 3, ...] = A066186.

Links

Robert Price, Table of n, a(n) for n = 1..1275, 50 rows.

Formula

Infinite lower triangular matrix, partition numbers (A000041, starting 1, 2, 3, 5, 7, 11, ...) in the main diagonal and the rest zeros.

Example

First few rows of the triangle:
  1;
  0, 2;
  0, 0, 3;
  0, 0, 0, 5;
  0, 0, 0, 0, 7;
  0, 0, 0, 0, 0, 11;
  ...

Mathematica

Table[Join[ConstantArray[0, n - 1], {PartitionsP[n]}], {n, 13}] // Flatten (* Robert Price, May 19 2020 *)
Table[Join[PadRight[{}, n-1, 0], {PartitionsP[n]}], {n, 20}]//Flatten (* Harvey P. Dale, Sep 14 2021 *)

Crossrefs

Cf. A000041, A066186.

Sequence in context: A127648 A212209 A259481 * A259480 A280164 A049597

Adjacent sequences: A132822 A132823 A132824 * A132826 A132827 A132828

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 02 2007

Status

approved