A078033 Expansion of (1-x) / (1+x^2+2*x^3).

1, -1, -1, -1, 3, 3, -1, -9, -5, 11, 23, -1, -45, -45, 47, 135, 43, -229, -313, 143, 771, 483, -1057, -2025, 91, 4139, 3959, -4321, -12237, -3597, 20879, 28071, -13685, -69829, -42457, 97199, 182115, -12285, -376513, -351945, 401083, 1104971, 302807, -1907137, -2512749, 1301523, 6327023

Offset

0,5

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,-1,-2).

Formula

2*((-1)^n)*a(n) + A001607(n+2) = 1 - Creighton Dement, Oct 30 2004

a(n) = -a(n-2) - 2*a(n-3) for n>2. - Colin Barker, May 18 2019

Maple

seq(coeff(series((1-x)/((1+x)*(1-x+2*x^2)), x, n+1), x, n), n = 0..40); # G. C. Greubel, Nov 22 2019

Mathematica

LinearRecurrence[{0, -1, -2}, {1, -1, -1}, 40] (* G. C. Greubel, Nov 22 2019 *)
CoefficientList[Series[(1-x)/(1+x^2+2x^3), {x, 0, 60}], x] (* Harvey P. Dale, Mar 31 2023 *)

Prog

(PARI) Vec((1-x)/((1+x)*(1-x+2*x^2)) + O(x^40)) \\ Colin Barker, May 18 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/((1+x)*(1-x+2*x^2)) )); // G. C. Greubel, Nov 22 2019
(Sage)
def A078033_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/((1+x)*(1-x+2*x^2)) ).list()
A078033_list(40) # G. C. Greubel, Nov 22 2019
(GAP) a:=[1, -1, -1];; for n in [4..40] do a[n]:=-a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Nov 22 2019

Crossrefs

Sequence in context: A350253 A262143 A284554 * A221712 A193741 A193824

Adjacent sequences: A078030 A078031 A078032 * A078034 A078035 A078036

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved