A141450 Upper right triangle of the number of m's in all partitions of n.

1, 1, 2, 1, 1, 4, 1, 1, 3, 7, 1, 1, 2, 4, 12, 1, 1, 2, 4, 8, 19, 1, 1, 2, 3, 6, 11, 30, 1, 1, 2, 3, 6, 9, 19, 45, 1, 1, 2, 3, 5, 8, 15, 26, 67, 1, 1, 2, 3, 5, 8, 13, 21, 41, 97, 1, 1, 2, 3, 5, 7, 12, 18, 31, 56, 139, 1, 1, 2, 3, 5, 7, 12, 17, 28, 45, 83, 195, 1, 1, 2, 3, 5, 7, 11, 16, 25, 38, 63

Offset

1,3

Comments

The "last" column read from the bottom is A000041.

Mirror of triangle A066633. - Omar E. Pol, May 01 2012

Links

Table of n, a(n) for n=1..89.

Example

A000070: 1, 2, 4, 7, 12, 19, 30, 45, 67, 97, 139, 195, 272, 373, 508, ...,
A024786: 0, 1, 1, 3, 4, 8, 11, 19, 26, 41, 56, 83, 112, 160, 213, ...,
A024787: 0, 0, 1, 1, 2, 4, 6, 9, 15, 21, 31, 45, 63, 87, 122, ...,
A024788: 0, 0, 0, 1, 1, 2, 3, 6, 8, 13, 18, 28, 38, 55, 74, ...,
A024789: 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 12, 17, 25, 35, 50, ...,
A024790: 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 16, 24, 33, ...,
A024791: 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 16, 23, ...,
A024792: 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, ...,
A024793: 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, ...,
A024794: 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, ...

Mathematica

(* First do ) Needs["Combinatorica`"] (* then *) f[n_, m_] := Count[Flatten@ Partitions@ n, m]; Table[ f[n, m], {n, 13}, {m, n, 1, -1}]

Crossrefs

Cf. A000041, A000070, A024786, A024787, A024788, A024789, A024790, A024791, A024792, A024793, A024794.

Sequence in context: A099238 A306846 A327315 * A209690 A061462 A294334

Adjacent sequences: A141447 A141448 A141449 * A141451 A141452 A141453

Keyword

nonn,tabl

Author

Robert G. Wilson v, Aug 07 2008

Status

approved