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

0,3

Links

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

Example

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

Maple

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

Crossrefs

Cf. A336482, A336512.

Sequence in context: A136488 A045621 A026655 * A244398 A100938 A018004

Adjacent sequences: A336481 A336482 A336483 * A336485 A336486 A336487

Keyword

nonn

Author

Alois P. Heinz, Jul 22 2020

Status

approved