A097062 Interleave 2*n+1 and 2*n-1.

1, -1, 3, 1, 5, 3, 7, 5, 9, 7, 11, 9, 13, 11, 15, 13, 17, 15, 19, 17, 21, 19, 23, 21, 25, 23, 27, 25, 29, 27, 31, 29, 33, 31, 35, 33, 37, 35, 39, 37, 41, 39, 43, 41, 45, 43, 47, 45, 49, 47, 51, 49, 53, 51, 55, 53, 57, 55, 59, 57, 61, 59, 63, 61, 65, 63, 67, 65, 69, 67, 71, 69, 73, 71, 75, 73, 77, 75, 79, 77, 81, 79, 83, 81, 85, 83, 87, 85

Offset: 0

Author

Paul Barry, Jul 22 2004

Keywords

• sign
• easy

Comments

Partial sums are A097063, whose pairwise sums are A002061.

Binomial transform is A097064.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A005408, A097063, A097064.

Programs

Haskell

import Data.List (transpose)
a097062 n = a097062_list !! n
a097062_list = concat $ transpose [a005408_list, (-1) : a005408_list]
-- Reinhard Zumkeller, Apr 16 2015

Magma

[(2*n-1)/2 + 3*(-1)^n/2 : n in [0..100]]; // Wesley Ivan Hurt, May 22 2021

Mathematica

LinearRecurrence[{1, 1, -1}, {1, -1, 3}, 100] (* Amiram Eldar, May 21 2021 *)
With[{nn=91},Riffle[Range[1,nn,2],Range[-1,nn-2,2]]] (* Harvey P. Dale, Jan 23 2023 *)

PARI

a(n)=(2*n-1)/2+3*(-1)^n/2 \\ Charles R Greathouse IV, Oct 07 2015

PARI

Vec((1-2*x+3*x^2)/((1-x^2)*(1-x)) + O(x^100)) \\ Altug Alkan, Nov 13 2015

Formula

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

a(n) = (2*n-1)/2 + 3*(-1)^n/2.

a(n) = 2*(n-1) - a(n-1), with a(0)=1. - Vincenzo Librandi, Nov 16 2010

a(n) = n - 2 + 3*((n-1) mod 2). - Lechoslaw Ratajczak, May 21 2021

a(n) = a(n-1)+a(n-2)-a(n-3). - Wesley Ivan Hurt, May 21 2021