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

Author

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

Keywords

• nonn

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

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

Crossrefs

Cf. A055684.

Cf. A008615, A103221.

Programs

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

Formula

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

Extensions

Edited by Andrew Baxter, Jun 06 2008