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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 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.)