|
|
A215123
|
|
Number of solid standard Young tableaux of shape [[n^2,n],[n]].
|
|
3
|
|
|
1, 2, 174, 52808, 31497284, 31113230148, 46190668836656, 96484621769643360, 270280816277448460968, 979042561410295182717884, 4456728497956906393963534248, 24916868994347706845906490576432, 167903137478620963997932010166057408
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
b:= proc(x, y, z) option remember; `if`(z<y, b(x, z, y),
`if`({x, y, z}={0}, 1, `if`(x>y and x>z, b(x-1, y, z), 0)+
`if`(y>0, b(x, y-1, z), 0)+ `if`(z>0, b(x, y, z-1), 0)))
end:
a:= n-> b(n^2, n, n):
seq(a(n), n=0..15);
|
|
MATHEMATICA
|
$RecursionLimit = 1000; b[x_, y_, z_] := b[x, y, z] = If[z<y, b[x, z, y], If[Union[{x, y, z}] == {0}, 1, If[x>y && x>z, b[x-1, y, z], 0] + If[y>0, b[x, y-1, z], 0] + If[z>0, b[x, y, z-1], 0]]]; a[n_] := b[n^2, n, n]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 05 2015, after Alois P. Heinz *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|