A395282 a(n) = Sum_{d|n} mu(d)*Fibonacci(2*(n/d)+1).

2, 3, 11, 29, 87, 217, 608, 1563, 4168, 10854, 28655, 74763, 196416, 513616, 1346169, 3522981, 9227463, 24153416, 63245984, 165569166, 433493816, 1134874510, 2971215071, 7778665461, 20365010985, 53316094752, 139583858264, 365434781904, 956722026039, 2504729424618

Offset

1,1

Comments

a(n) is the number of primitive rhythms of length n (see Romero-García et al.).

Links

Table of n, a(n) for n=1..30.

Gonzalo Romero-García, Lama Tarsissi, Laurent Najman, and Carlos Agon, Counting rhythms using combinatorics on words, hal-05582871, 2026. See Theorem 3 and Table 2 at pages 11-12.

Mathematica

a[n_]:=Sum[MoebiusMu[d]*Fibonacci[2(n/d)+1], {d, Divisors[n]}]; Array[a, 30]

Prog

(PARI) a(n) = sumdiv(n, d, moebius(d)*fibonacci(2*n/d+1)); \\ Michel Marcus, Apr 19 2026

Crossrefs

Cf. A000045, A001519, A008683, A122367.

Sequence in context: A243896 A202211 A104081 * A267902 A003455 A103275

Adjacent sequences: A395279 A395280 A395281 * A395283 A395284 A395285

Keyword

nonn,easy

Author

Stefano Spezia, Apr 18 2026

Status

approved