OFFSET
0,1
COMMENTS
Period 4:repeat 6,1,2,5 = A131800(n-1).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,0,1,-2).
FORMULA
G.f.: ( -4 + 6*x + x^2 + 2*x^3 + 9*x^4 ) / ( (x-1)*(2*x-1)*(1+x)*(x^2+1) ). - R. J. Mathar, Jan 18 2011
a(n) = 2*a(n-1) + A131800(n+2).
a(n) = a(n-4) + 2^n.
a(n) = -2*A112030(n+1)/5 - (-1)^n/6 - 7/2 + 2^n/15. - R. J. Mathar, Jan 18 2011
a(n) = 2*a(n-1) + a(n-4) - 2*a(n-5). - Vincenzo Librandi, Jun 17 2012
EXAMPLE
a(1) = 2*(-4) + 6 = -2;
a(2) = 2*(-2) + 1 = -3;
a(3) = 2*(-3) + 2 = -4;
a(4) = 2*(-4) + 5 = -3;
a(5) = 2*(-3) + 6 = 0.
MAPLE
A112030 := proc(n) (2+(-1)^n)*(-1)^floor(n/2) ; end proc:
MATHEMATICA
CoefficientList[Series[(-4+6*x+x^2+2*x^3+9*x^4)/((x-1)*(2*x-1)*(1+x)*(x^2+1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 17 2012 *)
LinearRecurrence[{2, 0, 0, 1, -2}, {-4, -2, -3, -4, -3}, 40] (* Harvey P. Dale, Sep 06 2020 *)
PROG
(Magma)I:=[-4, -2, -3, -4, -3]; [n le 5 select I[n] else 2*Self(n-1)+Self(n-4)-2*Self(n-5): n in [1..40]]; // Vincenzo Librandi, Jun 17 2012
CROSSREFS
KEYWORD
sign,easy,less
AUTHOR
Paul Curtz, Jan 18 2011
STATUS
approved