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

Author

Antti Karttunen, Oct 28 2001

Keywords

• nonn
• easy

Comments

This permutation of N induces also such permutation of Z, that p(i)-i >= 0 for all i.

Examples

			G.f. = 2*x + 4*x^2 + x^3 + 8*x^4 + 6*x^5 + 12*x^6 + 3*x^7 + 16*x^8 + ...
		

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).

Crossrefs

Cf. also A065171. The siteswap sequence (deltas) is A065261.

Programs

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 */

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