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 A237770 Number of standard Young tableaux with n cells without a succession v, v+1 in a row. 9
 1, 1, 1, 2, 4, 9, 22, 59, 170, 516, 1658, 5583, 19683, 72162, 274796, 1082439, 4406706, 18484332, 79818616, 353995743, 1611041726, 7510754022, 35842380314, 174850257639, 871343536591, 4430997592209, 22978251206350, 121410382810005, 653225968918521 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A standard Young tableau (SYT) without a succession v, v+1 in a row is called a nonconsecutive tableau. Also the number of ballot sequences without two consecutive elements equal. A ballot sequence B is a string such that, for all prefixes P of B, h(i)>=h(j) for ij and l[i]>0 and (i=1 or l[i]>l[i-1]),        h(subsop(i=l[i]-1, l), i), 0), i=1..nops(l))))     end: g:= proc(n, i, l) `if`(n=0 or i=1, h([1\$n, l[]], 0),       `if`(i<1, 0, g(n, i-1, l)+       `if`(i>n, 0, g(n-i, i, [i, l[]]))))     end: a:= n-> g(n, n, []): seq(a(n), n=0..30); # second Maple program (counting ballot sequences): b:= proc(n, v, l) option remember;       `if`(n<1, 1, add(`if`(i<>v and (i=1 or l[i-1]>l[i]),        b(n-1, i, subsop(i=l[i]+1, l)), 0), i=1..nops(l))+        b(n-1, nops(l)+1, [l[], 1]))     end: a:= proc(n) option remember; forget(b); b(n-1, 1, [1]) end: seq(a(n), n=0..30); MATHEMATICA b[n_, v_, l_List] := b[n, v, l] = If[n<1, 1, Sum[If[i != v && (i == 1 || l[[i-1]] > l[[i]]), b[n-1, i, ReplacePart[l, i -> l[[i]]+1]], 0], {i, 1, Length[l]}] + b[n-1, Length[l]+1, Append[l, 1]]]; a[n_] := a[n] = b[n-1, 1, {1}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 06 2015, translated from 2nd Maple program *) CROSSREFS Cf. A000085 (all Young tableaux), A000957, A001181, A214021, A214087, A214159, A214875. Cf. A238126 (tableaux with one succession), A238127 (two successions). Cf. A264051, A264078. Sequence in context: A077003 A210726 A046917 * A187044 A193361 A294281 Adjacent sequences:  A237767 A237768 A237769 * A237771 A237772 A237773 KEYWORD nonn AUTHOR Joerg Arndt and Alois P. Heinz, Feb 13 2014 STATUS approved

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Last modified June 15 22:19 EDT 2019. Contains 324145 sequences. (Running on oeis4.)