OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,-4).
FORMULA
O.g.f.: A(x) = (1+2*x^2+4*x^3)/(1+4*x^4).
E.g.f.: A(x) = cos(x)*exp(-x) + sin(x)*exp(x).
2*a(n) = i*(1-i)^n-i*(1+i)^n + (-1-i)^n + (-1+i)^n with i=sqrt(-1). - R. J. Mathar, Jan 18 2011
MAPLE
A118434 := proc(n) I*(1-I)^n-I*(1+I)^n+(-1-I)^n+(-1+I)^n ; expand(%/2) ; end proc:
# R. J. Mathar, Jan 18 2011
MATHEMATICA
a[n_] := 2^(Floor[(n+1)/2]-3)*(-2*Mod[n, 8] + Mod[n+2 , 8] - Mod[n+3, 8] + 2*Mod[n+4, 8] - Mod[n+6, 8] + Mod[n+7, 8]); Table[a[n], {n, 0, 44}] (* Jean-François Alcover, May 23 2013 *)
PROG
(PARI) {a(n)=polcoeff((1+2*x^2+4*x^3)/(1+4*x^4+x*O(x^n)), n)}
(PARI) /* E.g.f.: */
{a(n)=local(x=X+X*O(X^n)); n!*polcoeff(cos(x)*exp(-x)+sin(x)*exp(x), n, X)}
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul D. Hanna, Apr 28 2006
STATUS
approved