A077948 Expansion of 1/(1-x-x^2+2*x^3).

1, 1, 2, 1, 1, -2, -3, -7, -6, -7, 1, 6, 21, 25, 34, 17, 1, -50, -83, -135, -118, -87, 65, 214, 453, 537, 562, 193, -319, -1250, -1955, -2567, -2022, -679, 2433, 5798, 9589, 10521, 8514, -143, -12671, -29842, -42227, -46727, -29270, 8457, 72641, 139638, 195365, 189721, 105810, -95199, -368831

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Comments

Row sums of Riordan array (1/(1-x^2), x*(1-2*x^2)/(1-x^2)), A117355. - Paul Barry, Mar 09 2006

Links

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

Crossrefs

Cf. A077971.

Programs

GAP

a:=[1,1,2];; for n in [4..60] do a[n]:= a[n-1]+a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jul 03 2019

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/(1-x-x^2+2*x^3) )); // G. C. Greubel, Jul 03 2019

Mathematica

CoefficientList[Series[1/(1-x-x^2+2x^3),{x,0,60}],x] (* or *) LinearRecurrence[{1,1,-2},{1,1,2},60] (* Harvey P. Dale, Mar 15 2013 *)

PARI

Vec(1/(1-x-x^2+2*x^3)+O(x^60)) \\ Charles R Greathouse IV, Sep 25 2012

Sage

(1/(1-x-x^2+2*x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Jul 03 2019

Formula

a(n) = Sum_{k=0..n} Sum_{j=0..n-k} C(j-(n-k)/2-1,j)*C(k,j)*(1+(-1)^(n-k))/2. - Paul Barry, Mar 09 2006

a(n) = a(n-1) + a(n-2) - 2*a(n-3). If defined by this recurrence, the sequence could be preceded by 0, 0. - Paul Curtz, Feb 17 2008