OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
From Wesley Ivan Hurt, May 27 2016: (Start)
G.f.: x*(1+2*x+x^3)/( (x-1)^2*(1+x^2) ).
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
a(n) = (1+i)*(4*n-4*n*i+i-1-i^(-n)+i^(1+n))/4 where i=sqrt(-1).
E.g.f.: (2 - sin(x) - cos(x) + (4*x - 1)*exp(x))/2. - Ilya Gutkovskiy, May 27 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)+1)*Pi/16 + log(2)/8. - Amiram Eldar, Dec 24 2021
MAPLE
A047508:=n->(1+I)*(4*n-4*n*I+I-1-I^(-n)+I^(1+n))/4: seq(A047508(n), n=1..100); # Wesley Ivan Hurt, May 27 2016
MATHEMATICA
Table[(1+I)*(4n-4*n*I+I-1-I^(-n)+I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 27 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 4, 6, 7]]; // Wesley Ivan Hurt, May 27 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved