A152889 Periodic sequence [1,0,4,0,0] of period 5.

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

Offset

0,3

Links

Table of n, a(n) for n=0..104.

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

Formula

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

O.g.f: (1+4z^2)/(1-z^5).

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

Crossrefs

Cf. A026048.

Sequence in context: A096623 A171914 A200627 * A216273 A327517 A376504

Adjacent sequences: A152886 A152887 A152888 * A152890 A152891 A152892

Keyword

easy,nonn

Author

Richard Choulet, Dec 14 2008

Extensions

More terms from Philippe Deléham, Dec 29 2008

Status

approved