|
| |
| |
|
|
|
2, 4, 1, 8, 6, 12, 3, 16, 10, 20, 5, 24, 14, 28, 7, 32, 18, 36, 9, 40, 22, 44, 11, 48, 26, 52, 13, 56, 30, 60, 15, 64, 34, 68, 17, 72, 38, 76, 19, 80, 42, 84, 21, 88, 46, 92, 23, 96, 50, 100, 25, 104, 54, 108, 27, 112, 58, 116, 29, 120, 62, 124, 31, 128, 66, 132, 33, 136, 70
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
This permutation of N induces also such permutation of Z, that p(i)-i >= 0 for all i.
|
|
|
LINKS
|
Colin Barker, Table of n, a(n) for n = 1..1000
Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.
Index entries for sequences that are permutations of the natural numbers
Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).
|
|
|
FORMULA
|
a(n) = A059893(A057115(A059893(n))).
a(2*k+2) = 4*k+4, a(4*k+1) = 4*k+2, a(4*k+3) = 2*k+1. - Ralf Stephan, Jun 10 2005
G.f.: x*(x^6+4*x^5+2*x^4+8*x^3+x^2+4*x+2) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - Colin Barker, Feb 18 2013
a(n) = 2*a(n-4) - a(n-8) for n>8. - Colin Barker, Oct 29 2016
a(n) = (11*n+1+(5*n-1)*(-1)^n-(n+3)*(1-(-1)^n)*(-1)^((2*n+3+(-1)^n)/4))/8. - Luce ETIENNE, Oct 20 2016
|
|
|
EXAMPLE
|
G.f. = 2*x + 4*x^2 + x^3 + 8*x^4 + 6*x^5 + 12*x^6 + 3*x^7 + 16*x^8 + ...
|
|
|
PROG
|
(PARI) Vec(x*(2+4*x+x^2+8*x^3+2*x^4+4*x^5+x^6)/((1-x)^2*(1+x)^2*(1+x^2)^2) + O(x^100)) \\ Colin Barker, Oct 29 2016
(PARI) {a(n) = if( n%2==0, n*2, n%4==1, n+1, n\2)}; /* Michael Somos, Nov 06 2016 */
|
|
|
CROSSREFS
|
Cf. also A065171. The siteswap sequence (deltas) is A065261.
Sequence in context: A258065 A065290 A065266 * A257794 A345881 A091894
Adjacent sequences: A065257 A065258 A065259 * A065261 A065262 A065263
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Antti Karttunen, Oct 28 2001
|
|
|
STATUS
|
approved
|
| |
|
|
