A127365 Signed repeated natural numbers.

0, 0, -1, -1, 2, 2, -3, -3, 4, 4, -5, -5, 6, 6, -7, -7, 8, 8, -9, -9, 10, 10, -11, -11, 12, 12, -13, -13, 14, 14, -15, -15, 16, 16, -17, -17, 18, 18, -19, -19, 20, 20, -21, -21, 22, 22, -23, -23, 24, 24, -25, -25, 26, 26, -27, -27, 28, 28, -29, -29, 30, 30, -31, -31

Offset: 0

Author

Paul Barry, Jan 11 2007

Keywords

• easy
• sign

Comments

Hankel transform of A093387.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,-2,0,-1).

Crossrefs

Cf. A004526, A093387.

Programs

Magma

[(n div 2)*(-1)^(n div 2): n in [0..100]]; // Vincenzo Librandi, Nov 18 2018

Maple

A127365:=n->floor(n/2)*(-1)^floor(n/2); seq(A127365(n), n=0..100); # Wesley Ivan Hurt, Nov 30 2013

Mathematica

With[{c=Table[n (-1)^n,{n,0,30}]},Riffle[c,c]] (* Harvey P. Dale, Jul 21 2013 *)
LinearRecurrence[{0, -2, 0, -1}, {0, 0, -1, -1}, 100] (* Vincenzo Librandi, Nov 18 2018 *)

Formula

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

a(n) = floor(n/2)*(sin(n*Pi/2) + cos(n*Pi/2)).

a(n) = floor(n/2)*(-1)^floor(n/2) = A004526(n)*(-1)^A004526(n). - Wesley Ivan Hurt, Dec 10 2013

E.g.f.: (x*cos(x) - (1 + x)*sin(x))/2. - Stefano Spezia, Jul 14 2024