A108413 Expansion of (1+x+5x^2+2x^3) / (1-4x^2+x^4).
1, 1, 1, -2, -5, 7, 19, -26, -71, 97, 265, -362, -989, 1351, 3691, -5042, -13775, 18817, 51409, -70226, -191861, 262087, 716035, -978122, -2672279, 3650401, 9973081, -13623482, -37220045, 50843527, 138907099, -189750626, -518408351, 708158977, 1934726305
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,-4,0,-1).
Crossrefs
Unsigned values are in A002531.
Programs
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Mathematica
a[ n_] := If[n<0, a[2-n], SeriesCoefficient[(1 + x + 5*x^2 + 2*x^3) / (1 + 4*x^2 + x^4), {x, 0, n}]]; (* Michael Somos, Sep 23 2024 *) -
PARI
Vec((1 + x + 5*x^2 + 2*x^3) / (1 + 4*x^2 + x^4) + O(x^40)) \\ Colin Barker, Sep 07 2017
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PARI
{a(n) = if(n<0, n=2-n); polcoeff( (1 + x + 5*x^2 + 2*x^3) / (1 + 4*x^2 + x^4) + x*O(x^n), n)}; /* Michael Somos, Sep 23 2024 */
Formula
a(0)=a(1)=a(2)=1, a(n)*a(n+3) - a(n+1)*a(n+2) = -3.
a(n) = -4*a(n-2) - a(n-4) for n>3. - Colin Barker, Sep 07 2017
Comments