A341020 INVERT transform of the binary weight.

1, 1, 2, 5, 10, 22, 48, 104, 224, 485, 1050, 2271, 4914, 10633, 23006, 49777, 107700, 233027, 504192, 1090901, 2360344, 5106990, 11049806, 23908060, 51728994, 111924129, 242166136, 523965997, 1133686030, 2452914922, 5307282140, 11483171904, 24845718294

Offset

0,3

Comments

Number of compositions of n into parts where there are A000120(k) sorts of part k.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2984

Formula

G.f.: 1 / (1 - Sum_{k>=1} A000120(k) * x^k).

Maple

h:= proc(n) option remember; add(j, j=Bits[Split](n)) end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i)*h(i), i=1..n))
    end:
seq(a(n), n=0..36);

Mathematica

h[n_] := h[n] = DigitCount[n, 2, 1];
a[n_] := a[n] = If[n == 0, 1,
     Sum[a[n - i]*h[i], {i, 1, n}]];
Table[a[n], {n, 0, 36}] (* Jean-François Alcover, Apr 14 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000120.

Sequence in context: A101399 A320650 A018109 * A123491 A329185 A232163

Adjacent sequences: A341017 A341018 A341019 * A341021 A341022 A341023

Keyword

nonn

Author

Alois P. Heinz, Feb 02 2021

Status

approved