OFFSET
1,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
From Wesley Ivan Hurt, May 27 2016: (Start)
G.f.: x*(2+2*x+2*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-1-i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1).
E.g.f.: (2 - cos(x) + 4*x*sinh(x) + (4*x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 - sqrt(2)*log(2*sqrt(2)+3)/16. - Amiram Eldar, Dec 25 2021
MAPLE
A047510:=n->(8*n-1-I^(2*n)-I^(-n)-I^n)/4: seq(A047510(n), n=1..100); # Wesley Ivan Hurt, May 27 2016
MATHEMATICA
Table[(8n-1-I^(2n)-I^(-n)-I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 27 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [2, 4, 6, 7]]; // Wesley Ivan Hurt, May 27 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved