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 A214087 Sum of the squares of numbers of nonconsecutive tableaux over all partitions of n. 3
 1, 1, 1, 2, 6, 21, 92, 489, 3000, 20970, 166714, 1467337, 14212491, 149992662, 1723338952, 21393028409, 285061374438, 4054622024814, 61301381208116, 982904573560309, 16672187358390360, 298389960090957330, 5617735345244596804, 110942937545014894799 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A standard Young tableau (SYT) where entries i and i+1 never appear in the same row is called a nonconsecutive tableau. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..40 T. Y. Chow, H. Eriksson and C. K. Fan, Chess tableaux, Elect. J. Combin., 11 (2) (2005), #A3. Wikipedia, Young tableau MAPLE b:= proc(l, t) option remember; local n, s; n, s:= nops(l), add(i, i=l); `if`(s=0, 1, add(`if`(t<>i and l[i]> `if`(i=n, 0, l[i+1]), b(subsop(i=l[i]-1, l), i), 0), i=1..n)) end: g:= (n, i, l)-> `if`(n=0 or i=1, b([l[], 1\$n], 0)^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..20); MATHEMATICA b[l_, t_] := b[l, t] = Module[{n = Length[l], s = Total[l]}, If[s == 0, 1, Sum[If[t != i && l[[i]] > If[i == n, 0, l[[i + 1]]], b[ReplacePart[l, i -> l[[i]] - 1], i], 0], {i, 1, n}]]]; g[n_, i_, l_] := If[n == 0 || i == 1, b[Join[l, Table[1, n]], 0]^2, If[i < 1, 0, Sum[g[n - i*j, i - 1, Join[l, Table[i, j]]], {j, 0, n/i}]]]; a[n_] := If[n < 2, 1, g[n, n, {}]]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 23 2018, translated from Maple *) CROSSREFS Cf. A108774, A237770. Sequence in context: A115089 A304196 A266328 * A183950 A001928 A005638 Adjacent sequences: A214084 A214085 A214086 * A214088 A214089 A214090 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 02 2012 STATUS approved

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Last modified August 4 13:35 EDT 2024. Contains 374921 sequences. (Running on oeis4.)