OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
G.f.: x^2*(3-x+2*x^2) / ( (x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011
From Wesley Ivan Hurt, May 26 2016: (Start)
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+3*i-3-i^(-n)+i^(1+n))/4 where i=sqrt(-1).
E.g.f.: (4 - sin(x) - cos(x) + (4*x - 3)*exp(x))/2. - Ilya Gutkovskiy, May 27 2016
Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/8 - (3-2*sqrt(2))*Pi/16. - Amiram Eldar, Dec 21 2021
MAPLE
A047444:=n->(1+I)*(4*n-4*n*I+3*I-3-I^(-n)+I^(1+n))/4: seq(A047444(n), n=1..100); # Wesley Ivan Hurt, May 26 2016
MATHEMATICA
Table[(1+I)*(4n-4*n*I+3*I-3-I^(-n)+I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)
LinearRecurrence[{2, -2, 2, -1}, {0, 3, 5, 6}, 70] (* Harvey P. Dale, Aug 26 2019 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [0, 3, 5, 6]]; // Wesley Ivan Hurt, May 26 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved