A078052 Expansion of (1-x)/(1+x+2*x^2+2*x^3).
1, -2, 0, 2, 2, -6, -2, 10, 6, -22, -10, 42, 22, -86, -42, 170, 86, -342, -170, 682, 342, -1366, -682, 2730, 1366, -5462, -2730, 10922, 5462, -21846, -10922, 43690, 21846, -87382, -43690, 174762, 87382, -349526, -174762, 699050, 349526, -1398102, -699050, 2796202, 1398102, -5592406, -2796202
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (-1,-2,-2)
Programs
-
Magma
I:=[1,-2,0]; [n le 3 select I[n] else -Self(n-1)-2*Self(n-2) -2*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Aug 17 2013
-
Mathematica
CoefficientList[Series[(1 - x) / (1 + x + 2 x^2 + 2 x^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 17 2013 *) LinearRecurrence[{-1,-2,-2},{1,-2,0},50] (* Harvey P. Dale, Mar 26 2015 *) -
PARI
a(n)=1/3*((-3+5*(-1)^n)/2*(-2)^floor(n/2)+2*(-1)^n); \\ Ralf Stephan, Aug 17 2013
Formula
a(n) = (1/3) * ((-3+5*(-1)^n)/2 * (-2)^floor(n/2) + 2*(-1)^n ). - Ralf Stephan, Aug 17 2013
a(0)=1, a(1)=-2, a(2)=0, a(n)=-a(n-1)-2*a(n-2)-2*a(n-3). - Harvey P. Dale, Mar 26 2015
Comments