A336484 Total number of left-to-right minima in all compositions of n.

0, 1, 2, 5, 10, 22, 45, 93, 190, 387, 783, 1583, 3191, 6422, 12907, 25916, 51993, 104245, 208902, 418466, 837994, 1677694, 3358127, 6720661, 13448413, 26908246, 53834890, 107699435, 215446685, 430970500, 862065453, 1724331779, 3448987855, 6898499386

Offset: 0

Author

Alois P. Heinz, Jul 22 2020

Keywords

• nonn

Examples

			a(4) = 10: (1)111, (1)12, (1)21, (2)(1)1, (2)2, (1)3, (3)(1), (4).
		

Links

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

Crossrefs

Cf. A336482, A336512.

Programs

Maple

b:= proc(n, m, c) option remember; `if`(n=0, c, add(
      b(n-j, min(m, j), c+`if`(j b(n, n+1, 0):
seq(a(n), n=0..50);

Mathematica

b[n_, m_, c_] := b[n, m, c] = If[n == 0, c, Sum[
     b[n - j, Min[m, j], c + If[j < m, 1, 0]], {j, 1, n}]];
a[n_] := b[n, n+1, 0];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Mar 19 2022, after Alois P. Heinz *)