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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
Programs
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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 *)
Formula
a(n) ~ c * d^n / sqrt(n), where d = 3.6921332109291502908930783402282652076342401140592914... and c = 0.27220098720735952890181498005903942865018992276116... - Vaclav Kotesovec, Feb 14 2021