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

Author

Gary W. Adamson, Sep 02 2007

Keywords

• nonn
• tabl

Comments

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

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

Examples

			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;
  ...
		

Links

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

Crossrefs

Cf. A000041, A066186.

Programs

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 *)

Formula

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