A117378 Expansion of (1-4*x)/(1-x+x^2).
1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3
Offset: 0
Links
- Tanya Khovanova, Recursive Sequences
- Index entries for linear recurrences with constant coefficients, signature (1,-1).
Crossrefs
Cf. A117377.
Programs
-
Magma
[(1+(-n mod 3))^(n mod 3)*(-1)^Floor((n+2)/3) : n in [0..100]]; // Wesley Ivan Hurt, Aug 31 2014
-
Maple
A117378:=n->(1+(-n mod 3))^(n mod 3)*(-1)^floor((n+2)/3): seq(A117378(n), n=0..100); # Wesley Ivan Hurt, Aug 31 2014
-
Mathematica
CoefficientList[Series[(1 - 4 x)/(1 - x + x^2), {x, 0, 200}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *) LinearRecurrence[{1,-1},{1,-3},100] (* Harvey P. Dale, Sep 27 2018 *)
Formula
G.f.: (1-4*x)/(1-x+x^2).
a(n) = Sum_{k=0..n} (-1)^(n-k) * ( C(k,n-k) + 4*C(k,n-k-1) ).
a(n) = a(n-1) - a(n-2) for n>1. [Philippe Deléham, Nov 03 2008]
a(n) = (1+(-n mod 3))^(n mod 3)*(-1)^floor((n+2)/3). - Wesley Ivan Hurt, Aug 31 2014
a(n) = (3*cos(n*Pi/3) - 7*sqrt(3)*sin(n*Pi/3))/3. - Wesley Ivan Hurt, Jun 23 2016
E.g.f.: (3*cos(sqrt(3)*x/2) - 7*sqrt(3)*sin(sqrt(3)*x/2))*exp(x/2)/3. - Ilya Gutkovskiy, Jun 27 2016
Comments