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A152892 Periodic sequence [0,3,1,0,1] of period 5. 2
0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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) = a(3) = 0, a(1) = 3 and a(2) = a(4) = 1.

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

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

a(n) = (1/10)*(3*(n mod 5) - ((n+1) mod 5) + 3*((n+2) mod 5) + 5*((n+3) mod 5) - 5*((n+4) mod 5)) for n >= 0. - Paolo P. Lava, Dec 15 2008

a(n) = (n^3 + 2*n^2) mod 5. - Gary Detlefs, Mar 20 2010

MAPLE

seq((n^3+2*n^2)mod 5, n=0..50); # Gary Detlefs, Mar 20 2010

MATHEMATICA

PadRight[{}, 120, {0, 3, 1, 0, 1}] (* Harvey P. Dale, Oct 04 2016 *)

CROSSREFS

Cf. A026053, A026068.

Sequence in context: A060096 A245756 A322512 * A193002 A122960 A242887

Adjacent sequences:  A152889 A152890 A152891 * A152893 A152894 A152895

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Dec 14 2008

STATUS

approved

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Last modified June 4 11:31 EDT 2020. Contains 334825 sequences. (Running on oeis4.)