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
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
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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
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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
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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
Comments