OFFSET
1,3
LINKS
Vincenzo Librandi, 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 Colin Barker, May 14 2012: (Start)
a(n) = (-1/4+i/4)*((6+6*i)+(1+i)*(-1)^n+(-i)^n+i*i^n)+2*n where i=sqrt(-1).
G.f.: x^2*(1+2*x+x^2+4*x^3)/((1-x)^2*(1+x)*(1+x^2)). (End)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Vincenzo Librandi, May 16 2012
Sum_{n>=2} (-1)^n/a(n) = Pi/8 + (2-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4. - Amiram Eldar, Dec 20 2021
MAPLE
A047460:=n->(-1/4+I/4)*((6+6*I)+(1+I)*I^(2*n)+(-I)^n+I*I^n)+2*n: seq(A047460(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016
MATHEMATICA
Select[Range[0, 3000], MemberQ[{0, 1, 3, 4}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *)
PROG
(Magma) I:=[0, 1, 3, 4, 8]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 16 2012
(PARI) my(x='x+O('x^100)); concat(0, Vec(x^2*(1+2*x+x^2+4*x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ Altug Alkan, Dec 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved