OFFSET
0,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).
FORMULA
a(n+1) - 2*a(n) = 0, 1, -1, 0, -1, 1, ... is the hexaperiodic A092220 (corrected Sep 24 2007).
O.g.f.: x^2*(1-x)/((1+x)*(1-2*x)*(1-x+x^2)). - R. J. Mathar, Nov 23 2007
a(n) = Sum_{k=0..n-2} A001045(n-k+1)*binomial(k,n-k-2). - Paul Barry, Apr 22 2009
a(n) = (1/18)*( 2^(n+1) + 4*(-1)^n - 3*((-1)^floor((n+1)/3) + (-1)^floor((n+2)/3)) ). - G. C. Greubel, Nov 21 2019
MAPLE
seq(coeff(series(x^2*(1-x)/((1+x)*(1-2*x)*(1-x+x^2)), x, n+1), x, n), n = 0..35); # G. C. Greubel, Nov 21 2019
MATHEMATICA
Table[(2*(-1)^n +2^n -3*((-1)^Floor[(n+1)/3] +(-1)^Floor[(n+2)/3])/2)/9, {n, 0, 35}] (* G. C. Greubel, Nov 21 2019 *)
PROG
(PARI) my(x='x+O('x^35)); concat([0, 0], Vec(x^2*(1-x)/((1+x)*(1-2*x)*(1-x+x^2)))) \\ G. C. Greubel, Nov 21 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 35); [0, 0] cat Coefficients(R!( x^2*(1-x)/((1+x)*(1-2*x)*(1-x+x^2)) )); // G. C. Greubel, Nov 21 2019
(Sage)
def A131666_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x^2*(1-x)/((1+x)*(1-2*x)*(1-x+x^2))).list()
A131666_list(35) # G. C. Greubel, Nov 21 2019
(GAP) a:=[0, 0, 1, 1];; for n in [5..35] do a[n]:=2*a[n-1]-a[n-3]+2*a[n-4]; od; a; # G. C. Greubel, Nov 21 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Sep 14 2007
STATUS
approved