A035399 Limit of the position of the n-th partition without repetition in the list of all integer partitions sorted in reverse lexicographic order.

1, 2, 3, 5, 6, 8, 9, 13, 14, 15, 20, 21, 22, 25, 31, 32, 33, 35, 36, 46, 47, 48, 50, 51, 54, 68, 69, 70, 72, 73, 75, 76, 81, 98, 99, 100, 102, 103, 105, 106, 111, 112, 120, 140, 141, 142, 144, 145, 147, 148, 152, 153, 154, 160, 163, 196, 197, 198, 200, 201, 203

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Wouter Meeussen, Table of n, a(n) for n = 1..207

Example

For i=5, the partitions of i are 5, 41, 32, 311, 221, 2111, 11111.
The partitions without repetition are at position 1,2 and 3, corresponding to the first three terms of the sequence.
For i=10, the partitions of i begin 10, 91, 82, 811, 73, 721, 7111, 64, 631, 622, ...
The partitions without repetition are at position 1,2,3,5,6,8,9, ...

Mathematica

it=Table[Flatten[Position[IntegerPartitions[n], q_List/;  Sort[q]==Union[q] , 1]], {n, 36, 36+2, 2}];
{{diffat}}=Position[Take[Last[it], Length[First[it] ] ] - First[it] , a_ /; (a!=0), 1, 1]; Take[First[it], diffat -1 ]

Crossrefs

Cf. A000009, A035400, A186130, A186131.

Sequence in context: A226806 A058588 A357742 * A354852 A153775 A173666

Adjacent sequences: A035396 A035397 A035398 * A035400 A035401 A035402

Keyword

nonn

Author

Olivier Gérard

Extensions

Example and explanations from Olivier Gérard, Feb 13 2011

Status

approved