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A123046
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Number of frieze patterns of length n under a certain group (see Pisanski et al. for precise definition).
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| 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).
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FORMULA
| See Maple program.
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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);
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CROSSREFS
| Sequence in context: A075813 A004032 A107952 * A087784 A174197 A071224
Adjacent sequences: A123043 A123044 A123045 * A123047 A123048 A123049
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 11 2006
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