OFFSET
1,2
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
G.f.: x^2*(2+x+x^2+4*x^3)/((1-x)^2*(1+x)*(1+x^2)). - Colin Barker, May 13 2012
a(n) = (-11-(-1)^n-(2-i)*(-i)^n-(2+i)*i^n+8*n)/4 where i=sqrt(-1). - Colin Barker, May 14 2012
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Vincenzo Librandi, May 16 2012
E.g.f.: (8 + sin(x) - 2*cos(x) + (4*x - 5)*sinh(x) + (4*x - 6)*cosh(x))/2. - Ilya Gutkovskiy, May 31 2016
Sum_{n>=2} (-1)^n/a(n) = (2-sqrt(2))*Pi/16 + log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 21 2021
MAPLE
A047456:=n->(-11-(-1)^n-(2-I)*(-I)^n-(2+I)*I^n+8*n)/4: seq(A047456(n), n=1..100); # Wesley Ivan Hurt, May 31 2016
MATHEMATICA
Select[Range[0, 300], MemberQ[{0, 2, 3, 4}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *)
PROG
(Magma) I:=[0, 2, 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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved