A152856 Periodic sequence [4,0,4,3,4] of period 5

4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4

Offset

0,1

Links

Table of n, a(n) for n=0..69.

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) = a(4) = 4, a(1) = 0 and a(3) = 3

a(n) = 3+(1/2-3/10*5^(1/2))*cos(2*n*Pi/5)+(-1/10*(4*(5+5^(1/2))^(1/2)-(5-5^(1/2))^(1/2))*2^(1/2))*sin(2*n*Pi/5)+(3/10*5^(1/2)+1/2)*cos(4*n*Pi/5)+(-1/10*((5+5^(1/2))^(1/2)+4*(5-5^(1/2))^(1/2))*2^(1/2))*sin(4*n*Pi/5)

o.g.f f(z) = (4+4*z^2+3*z^3+4*z^4)/(1-z^5)

Mathematica

PadRight[{}, 100, {4, 0, 4, 3, 4}] (* Harvey P. Dale, Jun 08 2014 *)

Crossrefs

A026042

Sequence in context: A367873 A016680 A062524 * A031362 A378012 A198414

Adjacent sequences: A152853 A152854 A152855 * A152857 A152858 A152859

Keyword

easy,nonn

Author

Richard Choulet, Dec 14 2008

Status

approved