A093718 - OEIS

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A093718

a(n) = (n mod 3)^(n mod 2).

3

1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2

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OFFSET

0,6

COMMENTS

Period 6: repeat [1, 1, 1, 0, 1, 2]. - Joerg Arndt, Jun 09 2013

LINKS

Table of n, a(n) for n=0..101.

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

FORMULA

a(n) = A010872(n)^A000035(n).

G.f.: ( -1-x^2-2*x^4+x^3 ) / ( (x-1)*(1-x+x^2)*(1+x+x^2) ). - R. J. Mathar, Jun 09 2013

a(n) = (n + 3) mod (2 + n mod 2) - Wesley Ivan Hurt, Aug 16 2014

From Wesley Ivan Hurt, Jun 23 2016: (Start)

a(n) = cos(n*Pi/6) * (6*cos(n*Pi/6)-3*cos(n*Pi/2)-sqrt(3)*sin(n*Pi/2))/3.

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5).

a(n) = a(n-6) for n>5. (End)

E.g.f.: cosh(x) - cosh(x/2)*sin(sqrt(3)*x/2)/sqrt(3) + cos(sqrt(3)*x/2)*sinh(x/2) + sinh(x). - Stefano Spezia, Jul 26 2024

MAPLE

A093718:=n->(n mod 3)^(n mod 2): seq(A093718(n), n=0..100); # Wesley Ivan Hurt, Aug 16 2014

MATHEMATICA

Table[Mod[n + 3, 2 + Mod[n, 2]], {n, 0, 100}] (* Wesley Ivan Hurt, Aug 16 2014 *)

LinearRecurrence[{1, -1, 1, -1, 1}, {1, 1, 1, 0, 1}, 120] (* Harvey P. Dale, Jan 17 2021 *)

PROG

(Magma) &cat [[1, 1, 1, 0, 1, 2]^^20]; // Wesley Ivan Hurt, Jun 23 2016

CROSSREFS

Cf. A000035, A010872, A093719.

Sequence in context: A321755 A052314 A271606 * A278839 A348653 A278287

Adjacent sequences: A093715 A093716 A093717 * A093719 A093720 A093721

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Apr 12 2004

STATUS

approved