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

0,1

Links

Table of n, a(n) for n=0..54.

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

Formula

a(n+5) = a(n) with a(0) = a(2) = 4, a(1) = a(4) = 1 and a(3) = 0 ;

o.g.f f(z) = (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)

a(n)=(1/5)*{-2*(n mod 5)+5*[(n+2) mod 5]-2*[(n+3) mod 5]+4*[(n+4) mod 5]}, with n>=0 [From Paolo P. Lava, Jan 09 2009]

Crossrefs

A026051

Sequence in context: A064221 A229672 A298568 * A143354 A324026 A171539

Adjacent sequences: A152887 A152888 A152889 * A152891 A152892 A152893

Keyword

easy,nonn

Author

Richard Choulet, Dec 14 2008

Status

approved