A084056 a(n) = -a(n-1) + a(n-2) + a(n-3), with a(0)=0, a(1)=1, a(2)=-3.

0, 1, -3, 4, -6, 7, -9, 10, -12, 13, -15, 16, -18, 19, -21, 22, -24, 25, -27, 28, -30, 31, -33, 34, -36, 37, -39, 40, -42, 43, -45, 46, -48, 49, -51, 52, -54, 55, -57, 58, -60, 61, -63, 64, -66, 67, -69, 70, -72, 73, -75, 76, -78, 79, -81, 82, -84, 85, -87, 88, -90

Offset: 0

Author

Paul Barry, May 09 2003

Keywords

• easy
• sign

Links

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

Crossrefs

Cf. A032766 (absolute values).

Programs

Magma

[((1-6*n)*(-1)^n-1)/4 : n in [0..100]]; // Zaki Khandaker, Jun 21 2015

Maple

A084056:=n->((1-6*n) * (-1)^n - 1)/4; seq(A084056(n), n=0..100); # Wesley Ivan Hurt, Nov 10 2013

Mathematica

Table[((1 - 6n)(-1)^n - 1)/4, {n,0,100}] (* Wesley Ivan Hurt, Nov 10 2013 *)
LinearRecurrence[{-1, 1, 1}, {0, 1, -3}, 101] (* T. D. Noe, Nov 11 2013 *)

PARI

concat(0, Vec(x*(2*x-1)/((x-1)*(x+1)^2) + O(x^100))) \\ Colin Barker, Jun 21 2015

Formula

a(n) = (1/4) * ((1-6*n) * (-1)^n - 1).

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

a(n) = 2*a(n-2) - a(n-4) = -(-1)^n * A032766(n) = A001057(n) - 2*A001057(n-1). - Ralf Stephan, Aug 18 2013

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

Extensions

Definition fixed by Ralf Stephan, Aug 18 2013