OFFSET
1,2
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
From Bruno Berselli, Jul 17 2012: (Start)
G.f.: x*(1+x+2*x^2+x^3+3*x^4)/((1+x)*(1-x)^2*(1+x^2)).
a(n) = 2*n-2-((-1)^n+i^(n*(n+1)))/2, where i=sqrt(-1). (End)
From Wesley Ivan Hurt, Jun 02 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
E.g.f.: (6 + sin(x) - cos(x) + (4*x - 3)*sinh(x) + (4*x - 5)*cosh(x))/2. - Ilya Gutkovskiy, Jun 02 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)-1)*Pi/16 + sqrt(2)*log(sqrt(2)+2)/4 - (sqrt(2)+1)*log(2)/8. - Amiram Eldar, Dec 23 2021
MAPLE
A047613:=n->2*n-2-(I^(2*n)+I^(n*(n+1)))/2: seq(A047613(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016
MATHEMATICA
Select[Range[120], MemberQ[{1, 2, 4, 5}, Mod[#, 8]] &] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 4, 5, 9}, 60] (* Bruno Berselli, Jul 17 2012 *)
PROG
From Bruno Berselli, Jul 17 2012: (Start)
(Magma) [n: n in [1..120] | n mod 8 in [1, 2, 4, 5]];
(Maxima) makelist(2*n-2-((-1)^n+%i^(n*(n+1)))/2, n, 1, 60);
(PARI) Vec((1+x+2*x^2+x^3+3*x^4)/((1+x)*(1-x)^2*(1+x^2))+O(x^60)) (End)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved