A341071 Number of compositions of 2n into n squarefree parts.

1, 1, 3, 7, 23, 76, 267, 932, 3263, 11410, 40028, 140955, 498467, 1769249, 6299282, 22485487, 80435919, 288275461, 1034862558, 3720499175, 13393720428, 48275699654, 174194970601, 629187941167, 2274710068067, 8230764250326, 29805342037721, 108009638665648

Offset

0,3

Links

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

Formula

a(n) ~ c * d^n / sqrt(n), where d = 3.6921332109291502908930783402282652076342401140592914... and c = 0.27220098720735952890181498005903942865018992276116... - Vaclav Kotesovec, Feb 14 2021

Maple

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(2*n, n):
seq(a(n), n=0..35);

Mathematica

b[n_, t_] := b[n, t] =
  If[n == 0, If[t == 0, 1, 0], If[t < 1, 0, Sum[
  If[SquareFreeQ[j], b[n - j, t - 1], 0], {j, 1, n}]]];
a[n_] := b[2n, n];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, May 26 2023, from Maple program *)

Crossrefs

Cf. A005117, A333047, A338464, A338465, A341072.

Sequence in context: A148711 A344775 A205481 * A148712 A208591 A104088

Adjacent sequences: A341068 A341069 A341070 * A341072 A341073 A341074

Keyword

nonn

Author

Alois P. Heinz, Feb 04 2021

Status

approved