OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
From Wesley Ivan Hurt, May 29 2016: (Start)
G.f.: x^2*(5+x+x^2+x^3) / ((x-1)^2*(1+x+x^2+x^3)).
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (4*n-1+i^(2*n)-(1+i)*i^(-n)-(1-i)*i^n)/2 where i=sqrt(-1).
E.g.f.: 1 - sin(x) - cos(x) - sinh(x) + 2*x*exp(x). - Ilya Gutkovskiy, May 30 2016
Sum_{n>=2} (-1)^n/a(n) = 5*log(2)/8 - (2*sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 23 2021
MAPLE
A047575:=n->(4*n-1+I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/2: seq(A047575(n), n=1..100); # Wesley Ivan Hurt, May 29 2016
MATHEMATICA
Select[Range[0, 120], MemberQ[{0, 5, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Jun 30 2011 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [0, 5, 6, 7]]; // Wesley Ivan Hurt, May 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved