A120421 Number of distinct ribbon Schur functions with n boxes; also the number of distinct multisets of partitions determined by all coarsenings of compositions of n.

1, 2, 3, 6, 10, 20, 36, 72, 135, 272, 528, 1052, 2080, 4160, 8244, 16508, 32896, 65770, 131328, 262632, 524744, 1049600, 2098176, 4196200, 8390620, 16781312, 33558291, 67116944, 134225920, 268451240, 536887296, 1073774376, 2147515424

Offset

1,2

Links

Table of n, a(n) for n=1..33.

Louis Billera, Hugh Thomas, and Stephanie van Willigenburg, Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions, arXiv:math/0405434 [math.CO], 2004-2005.

Louis Billera, Hugh Thomas, and Stephanie van Willigenburg, Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions, Adv. Math. 204: 204-240 (2006).

Martin Rubey, The number of ribbon Schur functions, arXiv:1008.2501 [math.CO], 2010.

Formula

Dirichlet G.f.: 2 C(s) S(s)/(C(s)+S(s)) where C(s)=Sum_{n>0} 2^{n-1} n^{-s} and S(s)=Sum_{n>0} 2^{floor(n/2)} n^{-s}. - Martin Rubey, Aug 17 2010

Example

a(4)=6 as the multisets are {4}, {4,31}, {4,22}, {4,31,22,211}, {4,31,31,211} and {4,31,31,22,211,211,211,1111}

Crossrefs

Cf. A005418.

Sequence in context: A331488 A052525 A006606 * A005418 A329699 A002215

Adjacent sequences: A120418 A120419 A120420 * A120422 A120423 A120424

Keyword

nonn

Author

Stephanie van Willigenburg (steph(AT)math.ubc.ca), Jul 09 2006

Extensions

Corrected and extended by Martin Rubey, Aug 17 2010

Status

approved