A065259 A057114 conjugated with A059893, inverse of A065260.

3, 1, 7, 2, 11, 5, 15, 4, 19, 9, 23, 6, 27, 13, 31, 8, 35, 17, 39, 10, 43, 21, 47, 12, 51, 25, 55, 14, 59, 29, 63, 16, 67, 33, 71, 18, 75, 37, 79, 20, 83, 41, 87, 22, 91, 45, 95, 24, 99, 49, 103, 26, 107, 53, 111, 28, 115, 57, 119, 30, 123, 61, 127, 32, 131, 65, 135, 34, 139

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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(A057114(A059893(n))).

a(2*k+1) = 4*k+3, a(4*k+2) = 4*k+1, a(4*k+4) = 2*k+2. - Ralf Stephan, Jun 10 2005

a(n) = (11*n+2-(5*n+6)*(-1)^n+(n-2)*(1+(-1)^n)*(-1)^((2*n-3-(-1)^n)/4))/8. - Luce ETIENNE, Oct 29 2016

From Colin Barker, Oct 29 2016: (Start)

a(n) = 2*a(n-4) - a(n-8) for n>8.

G.f.: x*(3 + x + 7*x^2 + 2*x^3 + 5*x^4 + 3*x^5 + x^6)/((1 - x)^2*(1 + x)^2*(1 + x^2)^2). (End)

Example

G.f. = 3*x + x^2 + 7*x^3 + 2*x^4 + 11*x^5 + 5*x^6 + 15*x^7 + 4*x^8 + ...

Prog

(PARI) Vec(x*(3+x+7*x^2+2*x^3+5*x^4+3*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, 2*n+1, n%4, n-1, n/2)}; /* Michael Somos, Nov 06 2016 */

Crossrefs

Sequence in context: A065263 A057114 A235800 * A065289 A065265 A235263

Adjacent sequences: A065256 A065257 A065258 * A065260 A065261 A065262

Keyword

nonn,easy

Author

Antti Karttunen, Oct 28 2001

Status

approved