A128115 Mobius inversion of A103221.

0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 3, 1, 3, 2, 2, 1, 4, 1, 3, 2, 3, 2, 5, 2, 5, 3, 3, 2, 4, 2, 6, 3, 4, 2, 7, 2, 7, 4, 4, 3, 8, 3, 7, 4, 5, 4, 9, 3, 6, 4, 6, 4, 10, 2, 10, 5, 6, 5, 8, 4, 11, 6, 7, 4, 12, 4, 12, 6, 7, 6, 10, 4, 13, 6, 9, 6, 14, 4, 10, 7, 9, 6, 15, 4, 12, 8, 10, 7, 12, 5, 16, 7

Offset

1,11

Comments

Number of uniform n-grammic crossed antiprisms.

Agrees with Mobius inversion of A008615 for n != 3. - Andrew Baxter, Jun 06 2008

Number of primitive equivalence classes of period 2n billiards on an equilateral triangle. - Andrew Baxter, Jun 06 2008

Links

Table of n, a(n) for n=1..98.

Andrew M. Baxter and Ron Umble, Periodic Orbits of Billiards on an Equilateral Triangle, Amer. Math. Monthly, 115 (No. 6, 2008), 479-491.

Formula

SUM_{d|n} mu(d) * A103221(n/d), where mu is Mobius function (A008683). - Andrew Baxter, Jun 06 2008

Maple

with(numtheory): A103221:=n->floor((n+2)/2)-floor((n+2)/3): A128115:=n->add(mobius(d)*A103221(n/d), d in divisors(n)): # Andrew Baxter, Jun 06 2008

Crossrefs

Cf. A055684.

Cf. A008615, A103221.

Sequence in context: A145672 A175024 A175023 * A091318 A198898 A003639

Adjacent sequences: A128112 A128113 A128114 * A128116 A128117 A128118

Keyword

nonn

Author

Paulo de Almeida Sachs (sachs6(AT)yahoo.de), Feb 15 2007

Extensions

Edited by Andrew Baxter, Jun 06 2008

Status

approved