login
A257164
Period 5 sequence: repeat [0, 2, 4, 1, 3].
1
0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2
OFFSET
0,2
COMMENTS
Label the vertices of a regular pentagon from 0..4 going clockwise. Then, starting at vertex "0", a(n) gives the order in which the vertices must be connected to draw a clockwise inscribed, 5-pointed star that remains unbroken during construction.
FORMULA
a(n) = (2n mod 5) = A010874(A005843(n)).
G.f.: x*(2+4*x+x^2+3*x^3)/(1-x^5).
Recurrence: a(n) = a(n-5).
a(n) = a(a(a(a(a(n))))).
a(-n) = A010874(3n) = a(a(a(n))).
Bisections: a(2n) = A010874(-n) = a(a(n)); a(2n+1) = A010874(2-n).
Trisections: a(3n) = A010874(n) = a(a(a(a(n)))); a(3n+1) = A010874(n+2); a(3n+2) = A010874(n-1).
EXAMPLE
0 -> 2 -> 4 -> 1 -> 3 -> ..repeat
MAPLE
A257164:=n->(2*n mod 5): seq(A257164(n), n=0..100);
MATHEMATICA
Mod[2 Range[0, 100], 5] (* or *)
CoefficientList[Series[x (2 + 4 x + x^2 + 3 x^3)/(1 - x^5), {x, 0, 100}], x]
LinearRecurrence[{0, 0, 0, 0, 1}, {0, 2, 4, 1, 3}, 105] (* or *)
NestList[# /. {0 -> 2, 1 -> 3, 2 -> 4, 3 -> 0, 4 -> 1} &, {0}, 104] // Flatten (* Robert G. Wilson v, Apr 30 2015 *)
PROG
(Magma) [(2*n mod 5) : n in [0..100]];
(PARI) a(n)=2*n%5 \\ Charles R Greathouse IV, Apr 21 2015
CROSSREFS
Cf. A005843.
Bisection of A010874.
Sequence in context: A050980 A053451 A254076 * A190555 A141843 A322169
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 16 2015
STATUS
approved