OFFSET
0,2
COMMENTS
Partial sums of A098178.
Also A042968 with the even terms repeated. - Michel Marcus, Apr 14 2015
Fixed points are [2,3,6,7,10,11,..] = A042964. - Wesley Ivan Hurt, Oct 13 2015
LINKS
Iain Fox, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
G.f.: (1+x)(1-x+x^2)/((1-x)^2(1+x^2)).
a(n) = sqrt(2)*sin(Pi*n/2+Pi/4)/2+n+1/2.
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4), n>3.
From Wesley Ivan Hurt, Apr 12 2015, Oct 13 2015: (Start)
a(n) = (2n+1-(-1)^((n+1)*(n+2)/2))/2.
E.g.f: (exp(-i*x)*((1+i) + (1-i)*exp(2*i*x) + exp((1+i)*x)*(2+4*x)))/4, where i = sqrt(-1). - Iain Fox, Oct 17 2018
MAPLE
A098180:=n->(2*n+1-(-1)^((n+1)*(n+2)/2))/2: seq(A098180(n), n=0..100); # Wesley Ivan Hurt, Apr 12 2015
MATHEMATICA
Table[(2 n + 1 - (-1)^((n + 1) (n + 2)/2))/2, {n, 0, 40}] (* Wesley Ivan Hurt, Apr 12 2015 *)
PROG
(Magma) [Floor((2*n+1-(-1)^((n+1)*(n+2)/2))/2): n in [0..80]]; // Vincenzo Librandi, Apr 13 2015
(PARI) first(n) = Vec((1+x)*(1-x+x^2)/((1-x)^2*(1+x^2)) + O(x^n)) \\ Iain Fox, Oct 17 2018
(PARI) a(n) = (2*n+1-(-1)^((n+1)*(n+2)/2))/2 \\ Iain Fox, Oct 17 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Aug 30 2004
STATUS
approved