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

%I A336484 #19 Mar 19 2022 12:45:10
%S A336484 0,1,2,5,10,22,45,93,190,387,783,1583,3191,6422,12907,25916,51993,
%T A336484 104245,208902,418466,837994,1677694,3358127,6720661,13448413,
%U A336484 26908246,53834890,107699435,215446685,430970500,862065453,1724331779,3448987855,6898499386
%N A336484 Total number of left-to-right minima in all compositions of n.
%H A336484 Alois P. Heinz, <a href="/A336484/b336484.txt">Table of n, a(n) for n = 0..1000</a>
%e A336484 a(4) = 10: (1)111, (1)12, (1)21, (2)(1)1, (2)2, (1)3, (3)(1), (4).
%p A336484 b:= proc(n, m, c) option remember; `if`(n=0, c, add(
%p A336484       b(n-j, min(m, j), c+`if`(j<m, 1, 0)), j=1..n))
%p A336484     end:
%p A336484 a:= n-> b(n, n+1, 0):
%p A336484 seq(a(n), n=0..50);
%t A336484 b[n_, m_, c_] := b[n, m, c] = If[n == 0, c, Sum[
%t A336484      b[n - j, Min[m, j], c + If[j < m, 1, 0]], {j, 1, n}]];
%t A336484 a[n_] := b[n, n+1, 0];
%t A336484 Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Mar 19 2022, after _Alois P. Heinz_ *)
%Y A336484 Cf. A336482, A336512.
%K A336484 nonn
%O A336484 0,3
%A A336484 _Alois P. Heinz_, Jul 22 2020