A139100 Triangle read by rows: row n lists all partitions of n in the order produced by the shell model of partitions A138151.

1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 2, 2, 3, 1, 2, 1, 1, 1, 1, 1, 1, 5, 3, 2, 4, 1, 2, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 6, 4, 2, 3, 3, 2, 2, 2, 5, 1, 3, 2, 1, 4, 1, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 5, 2, 4, 3, 3, 2, 2, 6, 1, 4, 2, 1, 3, 3, 1, 2, 2, 2, 1, 5, 1, 1, 3, 2, 1, 1, 4

Offset: 1

Author

Omar E. Pol, Apr 15 2008

Keywords

• nonn
• tabf
• less

Comments

See the integrated diagram of partitions in the entry A138138.

See A138151 for more information.

First 43 members = A026792.

Examples

			Triangle begins:
{(1)}
{(2), (1, 1)}
{(3), (2, 1), (1, 1, 1)}
{(4), (2, 2), (3, 1), (2, 1, 1), (1, 1, 1, 1)}
{(5), (3, 2), (4, 1), (2, 2, 1), (3, 1, 1), (2, 1, 1, 1), (1, 1, 1, 1, 1)}
		

Links

• Robert Price, Table of n, a(n) for n = 1..7043, 17 rows.

Crossrefs

Cf. A000041, A006128, A026792, A036036, A080576, A080577, A135010, A138121, A138135, A138136, A138137, A138138, A138151.

Programs

Mathematica

Table[If[n == 1, ConstantArray[{1}, i - n + 1],
   Map[(Join[#, ConstantArray[{1}, i - n]]) &,
    Cases[IntegerPartitions[n], x_ /; Last[x] != 1]]], {i, 7}, {n, i, 1, -1}]  // Flatten(* Robert Price, May 28 2020 *)