

A060840


Number of irreducible representations of symmetric group S_n whose degree is not divisible by 3.


2



1, 2, 3, 3, 6, 9, 9, 18, 9, 9, 18, 27, 27, 54, 81, 81, 162, 54, 54, 108, 162, 162, 324, 486, 486, 972, 27, 27, 54, 81, 81, 162, 243, 243, 486, 243, 243, 486, 729, 729, 1458, 2187, 2187, 4374, 1458, 1458, 2916, 4374, 4374, 8748, 13122, 13122, 26244, 405, 405, 810
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OFFSET

1,2


REFERENCES

I. G. MacDonald, On the degrees of the irreducible representations of symmetric groups, Bull. London Math. Soc. 3 (1971), 189192


LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..1000


FORMULA

If n = sum a_i*3^e[i] in base 3 where a_i is 0, 1, 2 then a(n) = product g(i) where if a(i) = 0 g(i) = 1, if a(i) = 1 g(i) = 3^i, if a(i) = 2 g(i) = 3^i * (3^i + 3) / 2


EXAMPLE

a(4) = 3 because the degrees for S_4 are 1,1,2,3,3 and by the formula: 4 in base 3 is 11 and a(4) = 1*3


MATHEMATICA

a[n_] := (id = IntegerDigits[n, 3]; lg = Length[id]; Times @@ Table[ Which[ id[[lgi]] == 0, 1, id[[lgi]] == 1, 3^i, True, 3^i*(3^i+3)/2], {i, lg1, 0, 1}]); Table[a[n], {n, 1, 56}] (* JeanFrançois Alcover, Apr 30 2013 *)


PROG

(Sage)
def A060840(n) : dig = n.digits(3); return prod([1, 3^m, 3^m*(3^m+3)//2][dig[m]] for m in xrange(len(dig)))
# Eric M. Schmidt, Apr 30 2013


CROSSREFS

Cf. A059867.
Sequence in context: A027100 A261090 A183560 * A276096 A074717 A218137
Adjacent sequences: A060837 A060838 A060839 * A060841 A060842 A060843


KEYWORD

nonn,easy


AUTHOR

Noam Katz (noamkj(AT)hotmail.com), May 02 2001


EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), May 10 2001


STATUS

approved



