A123046 Number of frieze patterns of length n under a certain group (see Pisanski et al. for precise definition).

0, 1, 4, 6, 23, 52, 194, 586, 2131, 7286, 26524, 95326, 350738, 1290556, 4798174, 17895736, 67127315, 252645136, 954510114, 3616814566, 13744183772, 52357696956, 199912348954, 764877654106, 2932035552786, 11258999068468, 43303860638644, 166799986203766

Offset

0,3

Links

Table of n, a(n) for n=0..27.

T. Pisanski, D. Schattschneider and B. Servatius, Applying Burnside's lemma to a one-dimensional Escher problem, Math. Mag., 79 (2006), 167-180. See G(n).

Formula

See Maple program.

Maple

V:=proc(n) local k, t1; t1:=0; for k in divisors(n) do t1 := t1+phi(k)*4^(n/k); od: t1; end;
H:=n-> if n mod 2 = 0 then (n/2)*4^(n/2); else 0; fi;
R:=proc(n) local k, t1; t1:=0; for k in divisors(n) do if k mod 2 = 0 then t1 := t1+phi(k)*4^(n/k); fi; od: t1; end;
A123046:=n->(V(n)+2*H(n)+R(n))/(4*n);

Crossrefs

Sequence in context: A075813 A107952 A004032 * A237748 A394346 A359863

Adjacent sequences: A123043 A123044 A123045 * A123047 A123048 A123049

Keyword

nonn

Author

N. J. A. Sloane, Nov 11 2006

Status

approved