OFFSET
1,1
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 Wesley Ivan Hurt, May 27 2016: (Start)
G.f.: x*(3+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) = (1+i)*(4*n-4*n*i+(i-1)*i^(2*n)+i^(1-n)-i^n)/4 where i=sqrt(-1).
E.g.f.: (2 + sin(x) - cos(x) + (4*x + 1)*sinh(x) + (4*x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016
From Wesley Ivan Hurt, Aug 10 2016: (Start)
a(n) = a(n-4) + 8 for n > 4.
a(4*k) = 8*k-1, a(4*k-1) = 8*k-2, a(4*k-2) = 8*k-4, a(4*k-3) = 8*k-5. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)-1)*Pi/16 - (sqrt(2)-1)*log(2)/8 + sqrt(2)*log(2-sqrt(2))/4. - Amiram Eldar, Dec 26 2021
MAPLE
A047514:=n->(1+I)*(4*n-4*n*I+(I-1)*I^(2*n)+I^(1-n)-I^n)/4: seq(A047514(n), n=1..100); # Wesley Ivan Hurt, May 27 2016
MATHEMATICA
Table[(1+I)*(4n-4n*I+(I-1)*I^(2n)+I^(1-n)-I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 27 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {3, 4, 6, 7, 11}, 100] (* Vincenzo Librandi, Aug 11 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [3, 4, 6, 7]]; // Wesley Ivan Hurt, May 27 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved