OFFSET
1,3
COMMENTS
Complement of numbers that are congruent to {3, 4, 5, 6} mod 8 (A047425). - Jaroslav Krizek, Dec 19 2009
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
a(n) = 3*n-4*floor((n-2)/4)-6+(-1)^n. - Gary Detlefs, Mar 27 2010
G.f.: x^2*(1+x+5*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Harvey P. Dale, Sep 05 2014
From Wesley Ivan Hurt, May 21 2016: (Start)
a(n) = (4n-5+i^(2n)+(1+i)*i^(-n)+(1-i)*i^n)/2 where i = sqrt(-1).
Sum_{n>=2} (-1)^n/a(n) = (5-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4 - Pi/16. - Amiram Eldar, Dec 20 2021
MAPLE
seq(3*n-4*floor((n-2)/4)-6+(-1)^n, n=1..61); # Gary Detlefs, Mar 27 2010
MATHEMATICA
Select[Range[0, 200], MemberQ[{0, 1, 2, 7}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 7, 8}, 200] (* Harvey P. Dale, Sep 05 2014 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 7]]; // Wesley Ivan Hurt, May 21 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved