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A086970 Fix 1, then exchange the subsequent odd numbers in pairs. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 22 18:55 EST 2019. Contains 329410 sequences. (Running on oeis4.)