OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
G.f.: x*(1+3*x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015
From Wesley Ivan Hurt, May 26 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (8*n-3+i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1).
E.g.f.: (2 - cos(x) + (4*x - 2)*sinh(x) + (4*x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+3)*Pi/16 + log(2)/4 + sqrt(2)*log(sqrt(2)-1)/8. - Amiram Eldar, Dec 24 2021
MAPLE
A047493:=n->(8*n-3+I^(2*n)-I^(-n)-I^n)/4: seq(A047493(n), n=1..100); # Wesley Ivan Hurt, May 26 2016
MATHEMATICA
Table[(8n-3+I^(2n)-I^(-n)-I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 4, 5, 7, 9}, 80] (* Harvey P. Dale, May 05 2018 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 4, 5, 7]]; // Wesley Ivan Hurt, May 26 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved