A093718 -id:A093718 - cp's OEIS frontend

A093719 a(n) = (n mod 2)^(n mod 3).

1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1

Offset: 0

Reinhard Zumkeller, Apr 12 2004

This is a periodic sequence with period 6. The repeating block is 1,1,0,1,0,1. - Michel Dekking, Sep 19 2020

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for characteristic functions
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Cf. A000035, A010872, A047235, A047273, A093718.

List([0..120],n->(n mod 2)^(n mod 3)); # Muniru A Asiru, Dec 19 2018

[(n mod 2)^(n mod 3): n in [0..100]]; // Wesley Ivan Hurt, Oct 13 2014

A093719:=n->(n mod 2)^(n mod 3): seq(A093719(n), n=0..40); # Wesley Ivan Hurt, Oct 13 2014

PadRight[{},120,{1,1,0,1,0,1}] (* Harvey P. Dale, Jun 26 2021 *)

A093719(n) = ((n%2)^(n%3)); \\ Antti Karttunen, Dec 19 2018

a(n) = A000035(n)^A010872(n).
a(A047273(n)) = 1, a(A047235(n)) = 0. [Reinhard Zumkeller, Oct 01 2008]
G.f.: -(x^5 + x^3 + x + 1)/(x^6 - 1). - Colin Barker, Apr 01 2013
E.g.f.: (2*cos(sqrt(3)*x/2)*cosh(x/2) + cosh(x))/3 + sinh(x). - Stefano Spezia, Jul 26 2024

A242112 a(n) = floor((2*n+6)/(5-(-1)^n)).

Original entry on oeis.org

1, 1, 2, 2, 3, 2, 4, 3, 5, 4, 6, 4, 7, 5, 8, 6, 9, 6, 10, 7, 11, 8, 12, 8, 13, 9, 14, 10, 15, 10, 16, 11, 17, 12, 18, 12, 19, 13, 20, 14, 21, 14, 22, 15, 23, 16, 24, 16, 25, 17, 26, 18, 27, 18, 28, 19, 29, 20, 30, 20, 31, 21, 32, 22, 33, 22, 34, 23, 35, 24, 36

Offset: 0

Wesley Ivan Hurt, Aug 21 2014

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

Cf. A010693, A093718.

[Floor((2*n+6)/(5-(-1)^n)) : n in [0..100]];

[IsEven(n) select 1+n/2 else 1+Floor(n/3): n in [0..80]]; // Bruno Berselli, Aug 22 2014

A242112:=n->floor((2*n+6)/(5-(-1)^n)): seq(A242112(n), n=0..100);

Table[Floor[(2 n + 6)/(5 - (-1)^n)], {n, 0, 100}]
LinearRecurrence[{0,1,0,0,0,1,0,-1},{1,1,2,2,3,2,4,3},80] (* Harvey P. Dale, Oct 24 2017 *)

a(n) = a(n-2) + a(n-6) - a(n-8).
a(n) = ( n+3 - A093718(n) ) / A010693(n).
From Robert Israel, Aug 22 2014: (Start)
a(n) = sqrt(3)/18*(sin(2*n*Pi/3)+sin(n*Pi/3)) + 1/6*(cos(2*n*Pi/3)-cos(n*Pi/3)) + (-1)^n*(2+n)/12 + 5*(n+2)/12.
G.f.: (1 + x + x^2 + x^3 + x^4)/(1 - x^2 - x^6 + x^8). (End)
a(n) = 1 + n/2 if n is even, otherwise a(n) = 1 + floor(n/3). - Bruno Berselli, Aug 22 2014

cp's OEIS Frontend

A093719 a(n) = (n mod 2)^(n mod 3).

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A242112 a(n) = floor((2*n+6)/(5-(-1)^n)).

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Magma

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