OFFSET
0,2
LINKS
FORMULA
G.f.: 1/(1 + 4*x + 8*x^2).
E.g.f.: (cos(2*x) - sin(2*x))/exp(2*x).
a(n) = -4*a(n-1) - 8*a(n-2).
a(n+4) = -64*a(n).
G.f.: 1/(1 + 4*x/(1 - 2*x/(1 + 2*x))) = 1 - 4*x/(1 + 2*x/(1 - 2*x/(1 + 4*x))). - Michael Somos, Jan 03 2013
a(n) = (-4)^n*hypergeom([1/2-n/2, -n/2], [-n], 2) for n >= 1. - Peter Luschny, Dec 17 2015
EXAMPLE
1 - 4*x + 8*x^2 - 64*x^4 + 256*x^5 - 512*x^6 + 4096*x^8 - 16384*x^9 + ...
MAPLE
A143462 := n -> `if`(n=0, 1, (-4)^n*hypergeom([1/2-n/2, -n/2], [-n], 2)):
seq(simplify(A143462(n)), n=0..29); # Peter Luschny, Dec 17 2015
MATHEMATICA
CoefficientList[Series[1/(1 + 4*x + 8*x^2), {x, 0, 30}], x] (* Jinyuan Wang, Mar 10 2020 *)
PROG
(PARI) {a(n) = (-64)^(n \ 4) * [1, -4, 8, 0][n%4 + 1]}
(PARI) {a(n) = n--; -2 * 2^n * ((-1 + I)^n + (-1 - I)^n)}
(PARI) {a(n) = n--; simplify( -4 * (2 * quadgen(8))^n * polchebyshev(n, 1, -1 / quadgen(8)))}
(Magma) I:=[1, -4]; [n le 2 select I[n] else -4 * Self(n-1) - 8 * Self(n-2): n in [1..30]]; // Vincenzo Librandi, Dec 17 2015
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Michael Somos, Aug 16 2008
STATUS
approved