OFFSET
1,2
LINKS
G. C. Greubel, 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 29 2016: (Start)
G.f.: x*(1+x+x^2+4*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-7+i^(2*n)+(1+2*i)*i^(-n)+(1-2*i)*i^n)/4 where i=sqrt(-1).
E.g.f.: (2 + 2*sin(x) + cos(x) + 4*(x - 1)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 29 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = 3*sqrt(2)*Pi/16 + log(2)/8 + sqrt(2)*log(3-2*sqrt(2))/16. - Amiram Eldar, Dec 23 2021
MAPLE
A047533:=n->(8*n-7+I^(2*n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4: seq(A047533(n), n=1..100); # Wesley Ivan Hurt, May 29 2016
MATHEMATICA
Table[(8n-7+I^(2n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 29 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 3, 7, 9}, 50] (* G. C. Greubel, May 29 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 2, 3, 7]]; // Wesley Ivan Hurt, May 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved