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A318558 Number of degrees of irreducible representations of symmetric group S_n that appear more than once. 0
0, 0, 1, 1, 2, 3, 4, 6, 10, 14, 20, 26, 35, 43, 49, 77, 103, 125, 174, 190, 274, 340, 430, 496, 686, 838, 1026, 1263, 1579, 1832, 2457, 2833, 3631, 4249, 5114, 6111, 7962, 9072, 11015, 12939, 16173, 18304, 23101, 26188, 31822, 37518, 45073, 51403, 63489, 71822 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

FORMULA

a(n) = A060437(n) - A060426(n). - Alois P. Heinz, Aug 29 2018

EXAMPLE

Number 4 has the following partitions: a) [4], b) [3, 1], c) [2, 2], d) [2, 1, 1], e) [1, 1, 1, 1]. For partition a the cardinality of standard Young tableaux is 1, for b 3, for c 2, for d 3 and for e 1, so multiple cardinalities are 1 and 3: two multiple cardinalities, i.e., 4th sequence element is 2.

PROG

(Sage Math)

r=""

lista=[]

lista_rip=[]

rip=0

for i in range(1, 35):

        l=Partitions(i)

        for p in l:

            nsc=StandardTableaux(p).cardinality()

            if nsc in lista:

                if nsc not in lista_rip:

                    lista_rip.append(nsc)

                    rip += 1

            else:

                lista.append(nsc)

        r = r+", "+str(rip)

        rip=0

        lista=[]

        lista_rip=[]

print(r)

CROSSREFS

Cf. A060240, A060426, A060437.

Sequence in context: A229863 A215255 A200928 * A256248 A089223 A240057

Adjacent sequences:  A318555 A318556 A318557 * A318559 A318560 A318561

KEYWORD

nonn

AUTHOR

Pierandrea Formusa, Aug 28 2018

EXTENSIONS

a(42)-a(49) from Alois P. Heinz, Aug 29 2018

STATUS

approved

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Last modified June 13 15:33 EDT 2021. Contains 345008 sequences. (Running on oeis4.)