A128115 - OEIS

%I #5 Feb 19 2019 20:54:39

%S 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,

%T 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,

%U 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

%N Mobius inversion of A103221.

%C Number of uniform n-grammic crossed antiprisms.

%C Agrees with Mobius inversion of A008615 for n != 3. - _Andrew Baxter_, Jun 06 2008

%C Number of primitive equivalence classes of period 2n billiards on an equilateral triangle. - _Andrew Baxter_, Jun 06 2008

%H Andrew M. Baxter and Ron Umble, <a href="http://arXiv.org/abs/math/0509292">Periodic Orbits of Billiards on an Equilateral Triangle</a>, Amer. Math. Monthly, 115 (No. 6, 2008), 479-491.

%F SUM_{d|n} mu(d) * A103221(n/d), where mu is Mobius function (A008683). - _Andrew Baxter_, Jun 06 2008

%p 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

%Y Cf. A055684.

%Y Cf. A008615, A103221.

%K nonn

%O 1,11

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

%E Edited by _Andrew Baxter_, Jun 06 2008