A168053 Expansion of (1-2*x^2-3*x^3)/((1-x)^2*(1+x+x^2)).
1, 1, -1, -3, -3, -5, -7, -7, -9, -11, -11, -13, -15, -15, -17, -19, -19, -21, -23, -23, -25, -27, -27, -29, -31, -31, -33, -35, -35, -37, -39, -39, -41, -43, -43, -45, -47, -47, -49, -51, -51, -53, -55, -55, -57, -59, -59, -61, -63, -63, -65, -67, -67, -69
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
Crossrefs
Cf. A168054.
Programs
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Magma
m:=55; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x^2-3*x^3)/((1-x)^2*(1+x+x^2)))); // Bruno Berselli, May 31 2013 -
Mathematica
LinearRecurrence[{1,0,1,-1},{1,1,-1,-3},60] (* Harvey P. Dale, Jan 15 2015 *) CoefficientList[Series[(1 - 2 x^2 - 3 x^3) / ((1 - x)^2 (1 + x + x^2)), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 08 2016 *)
Formula
a(n) = -(n^9 -45n^8 +846n^7 -8610n^6 +51345n^5 -181125n^4 +361584n^3 -361260n^2 +137264n -6720)/6720.
a(n) = A168054(n)/2^n.
Comments