A152890 Periodic sequence [4,1,4,0,1] of period 5.

4, 1, 4, 0, 1, 4, 1, 4, 0, 1, 4, 1, 4, 0, 1, 4, 1, 4, 0, 1, 4, 1, 4, 0, 1, 4, 1, 4, 0, 1, 4, 1, 4, 0, 1, 4, 1, 4, 0, 1, 4, 1, 4, 0, 1, 4, 1, 4, 0, 1, 4, 1, 4, 0, 1

Offset: 0

Author

Richard Choulet, Dec 14 2008

Keywords

• easy
• nonn
• less

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

Crossrefs

Cf. A026051.

Formula

a(n+5) = a(n).

G.f: (4+z+4*z^2+z^4)/(1-z^5).

a(n) = 2+(-1/5*5^(1/2)+1)*cos(2*n*Pi/5)+(2/5*2^(1/2)*(5-5^(1/2))^(1/2))*sin(2*n*Pi/5)+(1/5*5^(1/2)+1)*cos(4*n*Pi/5)+(-2/5*2^(1/2)*(5+5^(1/2))^(1/2))*sin(4*n*Pi/5)