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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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).

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" Adv. Math. 204: 204-240 (2006).

M. Rubey, The number of ribbon Schur functions [From Martin Rubey (martin.rubey(AT)math.uni-hannover.de), Aug 17 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} [From Martin Rubey (martin.rubey(AT)math.uni-hannover.de), 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: A008927 A052525 A006606 * A005418 A002215 A007562

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 (martin.rubey(AT)math.uni-hannover.de), Aug 17 2010

STATUS

approved

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Last modified September 23 21:30 EDT 2017. Contains 292392 sequences.