A225121 Number of standard Young tableaux with shapes corresponding to partitions into distinct parts with minimal difference 2.

1, 1, 1, 1, 4, 5, 15, 21, 56, 246, 525, 1573, 5764, 14092, 41405, 136995, 772552, 2148290, 8806629, 31679365, 155743665, 495240074, 2049655762, 7403470138, 32627363920, 207316068370, 784695179515, 3721285661481, 16967347935561, 82192321793926, 455572563875425

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..120

Wikipedia, Young tableau

Maple

h:= proc(l) local n; n:=nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+
      add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)
    end:
g:= proc(n, i, l) local s; s:=ceil(i*(i+2)/4);
      `if`(n=s, h([l[], seq(i-2*j, j=0..iquo(i-1, 2))]), `if`(n>s, 0,
       g(n, i-1, l)+`if`(i>n, 0, g(n-i, i-2, [l[], i]))))
    end:
a:= n-> g(n, n, []):
seq(a(n), n=0..35);  # Alois P. Heinz, Apr 29 2013

Mathematica

h[l_List] := Module[{n}, 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_List] := Module[{s}, s = Ceiling[i*(i+2)/4]; If[n==s, h[Join[l, Table[i-2*j, {j, 0, Quotient[i-1, 2]}]]], If[n>s, 0, g[n, i-1, l] + If[i>n, 0, g[n-i, i-2, Append[l, i]]]]]]; a[n_] := g[n, n, {}]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jul 02 2015, after  Alois P. Heinz *)

Crossrefs

Cf. A218293 (tableaux with shapes corresponding to partitions into distinct parts).

Cf. A000085 (standard Young tableaux for all shapes).

Sequence in context: A100234 A007390 A037955 * A267991 A225536 A084179

Adjacent sequences: A225118 A225119 A225120 * A225122 A225123 A225124

Keyword

nonn

Author

Joerg Arndt, Apr 29 2013

Status

approved