OFFSET
1,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
G.f.: x^2*(1+x+4*x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011
From Wesley Ivan Hurt, May 24 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (8*n-11+i^(2*n)+(1+2*i)*i^(-n)+(1-2*i)*i^n)/4, where i=sqrt(-1).
E.g.f.: (4 + 2*sin(x) + cos(x) + (4*x - 6)*sinh(x) + (4*x - 5)*cosh(x))/2. - Ilya Gutkovskiy, May 25 2016
Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + log(2)/2 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 20 2021
MAPLE
A047397:=n->(8*n-11+I^(2*n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4: seq(A047397(n), n=1..100); # Wesley Ivan Hurt, May 24 2016
MATHEMATICA
Table[(8n-11+I^(2n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 24 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 6, 8}, 70] (* Harvey P. Dale, Dec 31 2017 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 2, 6]]; // Wesley Ivan Hurt, May 24 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Wesley Ivan Hurt, May 24 2016
STATUS
approved