A336770 Total sum of the left-to-right minima in all compositions of n into distinct parts.

0, 1, 2, 7, 9, 18, 39, 54, 83, 133, 268, 337, 542, 754, 1148, 2058, 2689, 3909, 5607, 7945, 10965, 19024, 23838, 34840, 47332, 67121, 89006, 125571, 194513, 250634, 349001, 473018, 644107, 860595, 1164018, 1532321, 2327654, 2923772, 4022746, 5290310, 7188111

Offset

0,3

Links

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

Example

a(6) = 39 = 1+1+3+3+4+6+2+6+1+6+6: (1)23, (1)32, (2)(1)3, (2)3(1), (3)(1)2, (3)(2)(1), (2)4, (4)(2), (1)5, (5)(1), (6).

Maple

b:= proc(n, i, k) option remember; `if`(i<k or n>
      (2*i-k+1)*k/2, 0, `if`(n=0, [1, 0], b(n, i-1, k)+
      (p-> p+[0, p[1]*i/k])(b(n-i, min(n-i, i-1), k-1))))
    end:
a:= n-> add(b(n$2, k)[2]*k!, k=1..floor((sqrt(8*n+1)-1)/2)):
seq(a(n), n=0..40);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[i < k || n > (2i - k + 1) k/2, {0, 0}, If[n == 0, {1, 0}, b[n, i - 1, k] + Function[p, p + {0, p[[1]] i/k}][b[n - i, Min[n - i, i - 1], k - 1]]]];
a[n_] := Sum[b[n, n, k][[2]] k!, {k, 1, Floor[(Sqrt[8n + 1] - 1)/2]}];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jul 12 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000009, A000254, A003056, A032020, A336512, A336718, A336771.

Sequence in context: A079326 A055673 A177737 * A361706 A293645 A293646

Adjacent sequences: A336767 A336768 A336769 * A336771 A336772 A336773

Keyword

nonn

Author

Alois P. Heinz, Aug 04 2020

Status

approved