A336512 Total sum of the left-to-right minima in all compositions of n.

0, 1, 3, 8, 17, 38, 78, 162, 330, 672, 1355, 2736, 5503, 11058, 22191, 44507, 89198, 178697, 357852, 716440, 1434041, 2869935, 5742801, 11490298, 22988084, 45988166, 91995547, 184021931, 368093352, 736266262, 1472660452, 2945526806, 5891385159, 11783304479

Offset

0,3

Links

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

Example

a(4) = 1 + 1 + 1 + 2 + 1 + 2 + 1 + 3 + 1 + 4 = 17: (1)111, (1)12, (1)21, (2)(1)1, (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, min(m, j))), j=1..n))
    end:
a:= n-> b(n, 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, Min[m, j]]], {j, 1, n}]];
a[n_] := b[n, n + 1][[2]];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Mar 07 2022, after Alois P. Heinz *)

Crossrefs

Cf. A001563 (the same for permutations of [n]), A336484, A336511, A336516, A336770.

Sequence in context: A034481 A295061 A247374 * A046994 A058811 A101822

Adjacent sequences: A336509 A336510 A336511 * A336513 A336514 A336515

Keyword

nonn

Author

Alois P. Heinz, Jul 23 2020

Status

approved