A049400 Partial sums of rows of A047884. Young Tableaux by height.

1, 1, 2, 1, 3, 4, 1, 6, 9, 10, 1, 10, 21, 25, 26, 1, 20, 51, 70, 75, 76, 1, 35, 127, 196, 225, 231, 232, 1, 70, 323, 588, 715, 756, 763, 764, 1, 126, 835, 1764, 2347, 2556, 2611, 2619, 2620, 1, 252, 2188, 5544, 7990, 9096, 9415, 9486, 9495, 9496, 1, 462, 5798, 17424, 27908, 33231, 35135, 35596

Offset

1,3

Links

Seiichi Manyama, Rows n = 1..70, flattened (first 44 rows from Alois P. Heinz)

Index entries for sequences related to Young tableaux.

Example

1;
1,  2;
1,  3,   4;
1,  6,   9,  10;
1, 10,  21,  25,  26;
1, 20,  51,  70,  75,  76;
1, 35, 127, 196, 225, 231, 232;
1, 70, 323, 588, 715, 756, 763, 764;

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) option remember;
      `if`(n=0, h(l), `if`(i<1, 0, `if`(i=1, h([l[], 1$n]), g(n, i-1, l)+
      `if`(i>n, 0, g(n-i, i, [l[], i])))))
    end:
T:= (n, k)-> g(n, k, []):
seq(seq(T(n, k), k=1..n), n=1..12); # Alois P. Heinz, Apr 16 2012

Mathematica

Accumulate /@ Table[ Plus @@ NumberOfTableaux /@ Reverse /@ Union[ Sort /@ (Compositions[n - m, m] + 1)], {n, 1, 12}, {m, 1, n}] // Flatten (* Jean-François Alcover, Jan 29 2013, after Mathematica program for A047884 *)

Crossrefs

Cf. A000085, A007579, A007578, A007580, A049401, A293128.

Sequence in context: A154929 A249042 A262472 * A283524 A106382 A229287

Adjacent sequences: A049397 A049398 A049399 * A049401 A049402 A049403

Keyword

easy,nice,nonn,tabl

Author

Alford Arnold

Status

approved