A375677 Number of partitions of [n] into blocks whose largest element is >= the sum of the remaining block elements.

1, 1, 2, 5, 13, 40, 133, 485, 1887, 7872, 34648, 161108, 784195, 3999850, 21209261, 117164889, 669800056, 3968343015, 24252416366, 153029073580, 992860849454, 6632168652281, 45444519380882, 319738889742372, 2303340195173602, 17001774682931823, 128258904114067371

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Wikipedia, Partition of a set

Example

a(4) = 13: 123|4, 124|3, 12|34, 12|3|4, 134|2, 13|24, 13|2|4, 14|23, 1|23|4, 14|2|3, 1|24|3, 1|2|34, 1|2|3|4.

Maple

b:= proc(n, l) option remember;   `if`(n=0, 1,  `if`(n=1, 1,
      b(n-1, sort([l[], n])))+add(`if`(n<=l[j], `if`(n=1, 1,
      b(n-1, sort(subsop(j=l[j]-n, l)))), 0), j=1..nops(l)))
    end:
a:= n-> b(n, []):
seq(a(n), n=0..15);

Mathematica

b[n_, l_] := b[n, l] = If[n == 0, 1, If[n == 1, 1,
   b[n-1, Sort[Append[l, n]]]] + Sum[If[n <= l[[j]], If[n == 1, 1,
   b[n-1, Sort[ReplacePart[l, j -> l[[j]] - n]]]], 0], {j, 1, Length[l]}]];
a[n_] := b[n, {}];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 15}] (* Jean-François Alcover, Aug 29 2024, after Alois P. Heinz *)

Crossrefs

Cf. A000110, A375641.

Sequence in context: A149864 A149865 A174146 * A149866 A149867 A062704

Adjacent sequences: A375674 A375675 A375676 * A375678 A375679 A375680

Keyword

nonn

Author

Alois P. Heinz, Aug 23 2024

Status

approved