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A108774 Sum of the squares of numbers of chess tableaux over all partitions of n. 5
1, 1, 2, 2, 4, 8, 16, 48, 160, 448, 2048, 6400, 31232, 125952, 604160, 3119104, 15638528, 93478912, 550141952, 3367698432, 24049516544, 146207539200, 1203934593024, 7615928598528, 67190404415488, 468355947429888, 4196459066949632, 33260378783744000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
T. Y. Chow, H. Eriksson and C. K. Fan, Chess tableaux, Elect. J. Combin., 11 (2) (2005), #A3.
FORMULA
a(n) = Sum_{lambda : partitions(n)} chess(lambda)^2, where chess(k) is the number of standard Young tableaux (SYT) with cell(i,j)+i+j == 1 mod 2. - Alois P. Heinz, Jun 30 2012
MAPLE
b:= proc() option remember; local s; s:= add(i, i=args); `if`(s=0, 1,
add(`if`(irem(s+i-args[i], 2)=1 and args[i]>`if`(i=nargs, 0,
args[i+1]), b(subsop(i=args[i]-1, [args])[]), 0), i=1..nargs))
end:
g:= (n, i, l)-> `if`(n=0 or i=1, b(l[], 1$n)^2, `if`(i<1, 0,
add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))):
a:= n-> `if`(n<2, 1, g(n, n, [])):
seq(a(n), n=0..27); # Alois P. Heinz, Jul 01 2012
MATHEMATICA
b[args_List] := b[args] = Module[{s=Total[args], nargs=Length[args]}, If[s == 0, 1, Sum[If[Mod[s+i-args[[i]], 2] == 1 && args[[i]] > If[i == nargs, 0, args[[i+1]] ], b[ReplacePart[args, i -> args[[i]]-1]], 0], {i, 1, nargs}] ] ]; g[n_, i_, l_List] := g[n, i, l] = If[n == 0 || i == 1, b[Join[l, Array[1&, n]]]^2, If[i<1, 0, Sum[g[n-i*j, i-1, Join[l, Array[i&, j]]], {j, 0, n/i}] ] ]; a[n_] := If[n<2, 1, g[n, n, {}]]; Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Jun 08 2015, after Alois P. Heinz *)
CROSSREFS
Cf. A214087.
Sequence in context: A001137 A123593 A122748 * A063402 A175195 A369289
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 27 2005
EXTENSIONS
More terms from Alois P. Heinz, Jun 30 2012
STATUS
approved

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Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)