The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A089248 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A089248

a(n) is the sum of the odd degrees of the irreducible representations of the symmetric group S_n.
(history; published version)

#14 by Alois P. Heinz at Mon Sep 23 10:31:47 EDT 2024

STATUS

proposed

approved

#13 by Jean-François Alcover at Mon Sep 23 09:45:06 EDT 2024

STATUS

editing

proposed

#12 by Jean-François Alcover at Mon Sep 23 09:41:30 EDT 2024

MATHEMATICA

h[l_] := With[{n = Length[l]}, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i + 1, n}], {j, 1, l[[i]]}], {i, 1, n}]];

Total[l]!/

Product[Product[

1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i + 1, n}], {j,

1, l[[i]]}], {i, 1, n}]];

g[n_, i_, l_] :=

g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Array[1 &, n]]], If[i < 1, 0, Flatten@ Table[g[n - i*j, i - 1, Join[l, Array[i &, j]]], {j, 0, n/i}]]];

If[i < 1, 0,

Flatten@Table[

g[n - i*j, i - 1, Join[l, Array[i &, j]]], {j, 0, n/i}]]];

Discussion

Mon Sep 23

09:45

Jean-François Alcover: Mma code very slow beyond a(50)

#11 by Jean-François Alcover at Mon Sep 23 09:39:18 EDT 2024

MATHEMATICA

h[l_] := With[{n = Length[l]},

Total[l]!/

Product[Product[

1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i + 1, n}], {j,

1, l[[i]]}], {i, 1, n}]];

g[n_, i_, l_] :=

If[n == 0 || i == 1, h[Join[l, Array[1 &, n]]],

If[i < 1, 0,

Flatten@Table[

g[n - i*j, i - 1, Join[l, Array[i &, j]]], {j, 0, n/i}]]];

a[n_] := a[n] = If[n == 1, 1, Select[g[n, n, {}], OddQ] // Total];

Table[Print[n, " ", a[n]];

a[n], {n, 1, 50}] (* Jean-François Alcover, Sep 23 2024, after Alois P. Heinz in A060240 *)

STATUS

approved

editing

#10 by Peter Luschny at Fri Mar 06 15:48:09 EST 2020

STATUS

proposed

approved

#9 by G. C. Greubel at Fri Mar 06 14:43:09 EST 2020

STATUS

editing

proposed

#8 by G. C. Greubel at Fri Mar 06 14:43:06 EST 2020

CROSSREFS

Cf. A059867, A000085, A059867.

STATUS

proposed

editing

#7 by F. Chapoton at Fri Mar 06 14:13:22 EST 2020

STATUS

editing

proposed

#6 by F. Chapoton at Fri Mar 06 14:13:12 EST 2020

PROG

.... res = 0

.... for P in Partitions(n) :

........ deg = P.dimension()

........ if is_odd(deg) : res += deg

.... return res

end; # Eric M. Schmidt, Apr 28 2013

STATUS

approved

editing

Discussion

Fri Mar 06

14:13

F. Chapoton: use space for indentation in sage code

#5 by Joerg Arndt at Mon Apr 29 03:12:38 EDT 2013

STATUS

proposed

approved