A084060 a(n) = 1/2 + (1-6*n)*(-1)^n/2.

1, 3, -5, 9, -11, 15, -17, 21, -23, 27, -29, 33, -35, 39, -41, 45, -47, 51, -53, 57, -59, 63, -65, 69, -71, 75, -77, 81, -83, 87, -89, 93, -95, 99, -101, 105, -107, 111, -113, 117, -119, 123, -125, 129, -131, 135, -137, 141, -143, 147, -149, 153, -155, 159, -161, 165, -167, 171, -173, 177, -179

Offset: 0

Author

Paul Barry, May 11 2003

Keywords

• easy
• sign

Comments

abs(a(n+1)) = A047270(n).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (-1,1,1).

Crossrefs

Cf. A032766, A084056.

Programs

GAP

List([0..60], n-> (1 + (1-6*n)*(-1)^n)/2); # G. C. Greubel, Jan 03 2020

Magma

[1/2+(1-6*n)*(-1)^n/2: n in [0..60]]; // Vincenzo Librandi, Oct 26 2011

Maple

seq( (1 + (1-6*n)*(-1)^n)/2, n=0..60); # G. C. Greubel, Jan 03 2020

Mathematica

Table[(1 + (1-6*n)*(-1)^n)/2, {n,0,60}] (* G. C. Greubel, Jan 03 2020 *)
LinearRecurrence[{-1,1,1},{1,3,-5},100] (* Harvey P. Dale, Mar 05 2023 *)

PARI

vector(61, n, (1 - (7-6*n)*(-1)^n)/2) \\ G. C. Greubel, Jan 03 2020

Sage

[(1 + (1-6*n)*(-1)^n)/2 for n in (0..60)] # G. C. Greubel, Jan 03 2020

Formula

Unsigned version is sum of alternate terms of A032766 (numbers congruent to {0,1,3} mod 4): (1, 3, 4, 6, 7, 9, 10, 12, ...) such that a(n) = A032766(n-1) + A032766(n+1). - Gary W. Adamson, Sep 13 2007

G.f.: (1 + 4*x - 3*x^2 )/( (1-x)*(1+x)^2 ). - R. J. Mathar, Oct 25 2011

E.g.f.: (1+3*x)*cosh(x) - 3*x*sinh(x). - G. C. Greubel, Jan 03 2020