A122299 Expansion of x * (1-x) / ( 1 - 2*x - 3*x^2 + x^3 ).
0, 1, 1, 5, 12, 38, 107, 316, 915, 2671, 7771, 22640, 65922, 191993, 559112, 1628281, 4741905, 13809541, 40216516, 117119750, 341079507, 993301748, 2892722267, 8424270271, 24533405595, 71446899736, 208069745986, 605946785585, 1764655909392, 5139082429553
Offset: 1
Keywords
Links
- Muniru A Asiru, Table of n, a(n) for n = 1..500
- Index entries for linear recurrences with constant coefficients, signature (2,3,-1)
Programs
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GAP
a:=[0,1,1];; for n in [4..30] do a[n]:=2*a[n-1]+3*a[n-2]-a[n-3]; od; a; # Muniru A Asiru, Oct 07 2018
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Magma
I:=[0,1,1]; [n le 3 select I[n] else 2*Self(n-1)+3*Self(n-2)-Self(n-3): n in [1..30]]; // Vincenzo Librandi, Oct 08 2018
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Maple
seq(coeff(series(x*(1-x)/(1-2*x-3*x^2+x^3),x,n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 07 2018
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Mathematica
CoefficientList[Series[x*(1-x)/(1-2*x-3*x^2+x^3), {x,0,30}], x] (* G. C. Greubel, Oct 08 2018 *) LinearRecurrence[{2,3,-1},{0,1,1},40] (* Harvey P. Dale, Mar 11 2025 *) -
PARI
x='x+O('x^30); concat([0], Vec(x*(1-x)/(1-2*x-3*x^2+x^3))) \\ G. C. Greubel, Oct 08 2018
Formula
a(n)= +2*a(n-1) +3*a(n-2) -a(n-3).
Comments