A086970 Fix 1, then exchange the subsequent odd numbers in pairs.

1, 5, 3, 9, 7, 13, 11, 17, 15, 21, 19, 25, 23, 29, 27, 33, 31, 37, 35, 41, 39, 45, 43, 49, 47, 53, 51, 57, 55, 61, 59, 65, 63, 69, 67, 73, 71, 77, 75, 81, 79, 85, 83, 89, 87, 93, 91, 97, 95, 101, 99, 105, 103, 109, 107, 113, 111, 117, 115, 121, 119

Offset

0,2

Comments

Partial sums are A086955.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

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

a(n) = n + abs(2 - (n + 1)*(-1)^n). - Lechoslaw Ratajczak, Dec 09 2016

a(n) = 2*A065190(n+1)-1 and a(n) = 2*A014681(n)+1. - Michel Marcus, Dec 10 2016

From Guenther Schrack, Jun 09 2017: (Start)

a(n) = 2*n + 1 - 2*(-1)^n for n > 0.

a(n) = 2*n + 1 - 2*cos(n*Pi) for n > 0.

a(n) = 4*n - a(n-1) for n > 1.

Linear recurrence: a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3.

First differences: 2 - 4*(-1)^n for n > 1; -(-1)^n*A010696(n) for n > 1.

a(n) = A065164(n+1) + n for n > 0.

a(A014681(n)) = A005408(n) for n >= 0.

a(A005408(A014681(n)) for n >= 0.

a(n) = A005408(A103889(n)) for n >= 0.

A103889(a(n)) = 2*A065190(n+1) for n >= 0.

a(2*n-1) = A004766(n) for n > 0.

a(2*n+2) = A004767(n) for n >= 0. (End)

Mathematica

Join[{1}, LinearRecurrence[{1, 1, -1}, {5, 3, 9}, 60]] (* Vincenzo Librandi, Jun 21 2017 *)

Prog

(Magma) [1] cat [2*n+1-2*(-1)^n: n in [1..70]]; // Vincenzo Librandi, Jun 21 2017
(PARI) Vec((1+4*x-3*x^2+2*x^3)/((1+x)*(1-x)^2) + O(x^100)) \\ Michel Marcus, Jun 21 2017

Crossrefs

Cf. A004442, A014681, A065190.

Sequence in context: A242616 A073891 A196396 * A224511 A201938 A201410

Adjacent sequences: A086967 A086968 A086969 * A086971 A086972 A086973

Keyword

easy,nonn

Author

Paul Barry, Jul 26 2003

Status

approved