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

Author

Paul Barry, Jul 26 2003

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A004442, A014681, A065190.

Programs

Magma

[1] cat [2*n+1-2*(-1)^n: n in [1..70]]; // Vincenzo Librandi, Jun 21 2017

Mathematica

Join[{1}, LinearRecurrence[{1, 1, -1}, {5, 3, 9}, 60]] (* 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

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)