A065260 A057115 conjugated with A059893, inverse of A065259.

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

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 A372868

Adjacent sequences: A065257 A065258 A065259 * A065261 A065262 A065263

Keyword

nonn,easy

Author

Antti Karttunen, Oct 28 2001

Status

approved