A300183 Number of partitions of n whose minimal excluded multiplicity is odd.

1, 0, 1, 1, 3, 3, 5, 6, 11, 13, 18, 23, 36, 42, 60, 77, 103, 129, 171, 212, 280, 354, 443, 559, 709, 874, 1090, 1357, 1674, 2065, 2534, 3101, 3790, 4636, 5598, 6822, 8231, 9938, 11939, 14391, 17197, 20640, 24586, 29357, 34884, 41541, 49097, 58292, 68778, 81287

Offset

0,5

Links

Table of n, a(n) for n=0..49.

Formula

a(n) = A000041(n) - A299408(n).

Example

a(5) = 3: [1,1,1,1,1], [2,2,1], [3,1,1].
a(6) = 5: [1,1,1,1,1,1], [2,2,1,1], [2,2,2], [3,3], [4,1,1].
a(7) = 6: [1,1,1,1,1,1,1], [2,2,1,1,1], [3,2,1,1], [3,2,2], [3,3,1], [5,1,1].
a(11) = 23: [1,1,1,1,1,1,1,1,1,1,1], [2,2,1,1,1,1,1,1,1], [2,2,2,1,1,1,1,1], [2,2,2,2,1,1,1], [3,2,2,1,1,1,1], [3,3,1,1,1,1,1], [3,3,2,2,1], [3,3,3,1,1], [4,3,2,1,1], [4,3,2,2], [4,3,3,1], [4,4,1,1,1], [4,4,2,1], [4,4,3], [5,2,2,1,1], [5,3,3], [5,4,1,1], [5,5,1], [6,2,2,1], [6,3,1,1], [7,2,1,1], [7,2,2], [9,1,1].

Crossrefs

Cf. A000041, A299408.

Sequence in context: A091607 A276434 A183561 * A222704 A095950 A089874

Adjacent sequences: A300180 A300181 A300182 * A300184 A300185 A300186

Keyword

nonn

Author

Alois P. Heinz, Feb 27 2018

Status

approved