|
|
A065176
|
|
Site swap sequence associated with the permutation A065174 of Z.
|
|
5
|
|
|
0, 2, 2, 4, 4, 2, 2, 8, 8, 2, 2, 4, 4, 2, 2, 16, 16, 2, 2, 4, 4, 2, 2, 8, 8, 2, 2, 4, 4, 2, 2, 32, 32, 2, 2, 4, 4, 2, 2, 8, 8, 2, 2, 4, 4, 2, 2, 16, 16, 2, 2, 4, 4, 2, 2, 8, 8, 2, 2, 4, 4, 2, 2, 64, 64, 2, 2, 4, 4, 2, 2, 8, 8, 2, 2, 4, 4, 2, 2, 16, 16, 2, 2, 4, 4, 2, 2, 8, 8, 2, 2, 4, 4, 2, 2, 32, 32, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Here the site swap pattern ...,2,16,2,4,2,8,2,4,2,0,2,4,2,8,2,4,2,16,2,... that spans over the Z (zero throw is at t=0) has been folded to N by picking values at t=0, t=1, t=-1, t=2, t=-2, etc. successively.
This pattern is shown in the figure 7 of Buhler and Graham paper and uses infinitely many balls, with each ball at step t thrown always to constant "height" 2^A001511[abs(t)] (no balls in hands at step t=0).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1-x+x^2)/(1-x) + (1+x)*Sum(k>=1, 2^(k-1)*x^2^k/(1-x^2^k)). - Ralf Stephan, Apr 17 2003
|
|
MAPLE
|
[seq(TZ2(abs(N2Z(n))), n=1..120)]; # using TZ2 from A065174
N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1), 1, 0);
# Alternative:
A065176 := n -> `if`(n = 1, 0, 2^padic:-ordp(n - 1 + irem(n-1, 2), 2)):
|
|
PROG
|
(PARI) a(n) = if(n==1, 0, 1<<valuation(bitnegimply(n, 1), 2)); \\ Kevin Ryde, Jul 09 2021
(Python)
s, h = 1, n // 2
if 0 == h: return 0
while 0 == h % 2:
h //= 2
s += s
return s + s
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|