OFFSET
1,1
COMMENTS
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Maths Magic, Mystery Calculator.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
G.f.: x*(4+x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, May 19 2016: (Start)
a(n) = a(n-1)+a(n-4)-a(n-5) for n>5.
a(n) = (4*n+1-(-1)^n-(-1)^((n+1)/2)-(-1)^(n/2)-(-1)^(-(n+1)/2)-(-1)^(-n/2))/2. (End)
E.g.f.: 1 + sin(x) - cos(x) + sinh(x) + 2*x*exp(x). - Ilya Gutkovskiy, May 20 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)-1)*Pi/16 - 3*log(2)/8. - Amiram Eldar, Dec 26 2021
MAPLE
A047566:= n-> n+3 + 4*iquo(n-1, 4):
seq(A047566(n), n=1..100); # Alois P. Heinz, Aug 22 2011
MATHEMATICA
Flatten[# + {4, 5, 6, 7}&/@(8Range[0, 14])] (* Harvey P. Dale, Feb 02 2011 *)
PROG
(Haskell)
a047566 n = a047566_list !! (n-1)
a047566_list = [n | n <- [1..], mod n 8 > 3]
-- Reinhard Zumkeller, Dec 29 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved