A336511 Total sum of the left-to-right maxima in all compositions of n.

0, 1, 3, 9, 22, 52, 117, 260, 565, 1217, 2593, 5487, 11538, 24146, 50316, 104490, 216337, 446754, 920506, 1892904, 3885719, 7964162, 16300646, 33321640, 68038796, 138784403, 282824924, 575866839, 1171612786, 2381938742, 4839331484, 9825841526, 19938975797

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

a(4) = 1 + 1 + 2 + 1 + 2 + 2 + 2 + 1 + 3 + 3 + 4 = 22: (1)111, (1)1(2), (1)(2)1, (2)11, (2)2, (1)(3), (3)1, (4).

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0], add((p-> [0,
      `if`(j>m, j*p[1], 0)]+p)(b(n-j, max(m, j))), j=1..n))
    end:
a:= n-> b(n, -1)[2]:
seq(a(n), n=0..50);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, {0,
     If[j > m, j*p[[1]], 0]} + p][b[n - j, Max[m, j]]], {j, 1, n}]];
a[n_] := b[n, -1][[2]];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Mar 04 2022, after Alois P. Heinz *)

Crossrefs

Cf. A001705 (the same for permutations of [n]), A336482, A336512, A336516, A336771.

Sequence in context: A305612 A202882 A350105 * A054442 A354648 A192663

Adjacent sequences: A336508 A336509 A336510 * A336512 A336513 A336514

Keyword

nonn

Author

Alois P. Heinz, Jul 23 2020

Status

approved