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

1,2

Comments

See the integrated diagram of partitions in the entry A138138.

See A138151 for more information.

First 43 members = A026792.

Links

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

Example

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)}

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 *)

Crossrefs

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

Sequence in context: A277648 A026792 A334301 * A237982 A239512 A334439

Adjacent sequences: A139097 A139098 A139099 * A139101 A139102 A139103

Keyword

nonn,tabf,less

Author

Omar E. Pol, Apr 15 2008

Status

approved