OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
From Wesley Ivan Hurt, May 29 2016: (Start)
G.f.: x*(1+2*x+3*x^2+x^3+x^4) / ((x-1)^2*(1+x+x^2+x^3)).
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (8*n-3-i^(2*n)-i^(1-n)+i^(1+n))/4 where i=sqrt(-1).
E.g.f.: (2 - sin(x) + (4*x - 1)*sinh(x) + (4*x - 2)*cosh(x))/2. - Ilya Gutkovskiy, May 30 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (2+sqrt(2))*Pi/16 + sqrt(2)*log(2+sqrt(2))/8 - (2+sqrt(2))*log(2)/16. - Amiram Eldar, Dec 24 2021
MAPLE
A047558:=n->(8*n-3-I^(2*n)-I^(1-n)+I^(1+n))/4: seq(A047558(n), n=1..100); # Wesley Ivan Hurt, May 29 2016
MATHEMATICA
Select[Range[150], MemberQ[{1, 3, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Jul 31 2014 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 3, 6, 7]]; // Wesley Ivan Hurt, May 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved