A165211 Period 8: repeat [0,1,0,1,1,0,1,0].

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

Offset: 0

Author

Philippe Deléham, Sep 07 2009

Keywords

• nonn
• easy

Comments

Parity of A064706.

Parity of the generalized pentagonal numbers A001318. - Omar E. Pol, Feb 04 2012

More generally, parity of the generalized k-gonal numbers, for odd k >= 5. - Omar E. Pol, Feb 05 2012

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1).

Crossrefs

Cf. A001318, A002817, A064706.

Cf. A130198 (essentially the same).

Programs

Mathematica

PadRight[{},112,{0,1,0,1,1,0,1,0}] (* Harvey P. Dale, Jan 29 2012 *)
Table[Mod[n*(n+1)*(n^2+n+2)/8,2],{n,0,100}] (* Vaclav Kotesovec, Apr 28 2014 after Wesley Ivan Hurt *)

PARI

a(n)=bitxor(n, n\4)%2 \\ Charles R Greathouse IV, Jul 13 2016

PARI

concat(0, Vec(x*(1 - x + x^2) / ((1 - x)*(1 + x^4)) + O(x^100))) \\ Colin Barker, Dec 20 2017

Python

def A165211(n): return n&1^bool(n&4) # Chai Wah Wu, Aug 30 2024

Formula

a(n) = A002817(n) mod 2. - Wesley Ivan Hurt, Apr 23 2014

a(n) = 1/2 - (-1)^(n*(n+1)*(n^2 + n + 2)/8)/2. - Vaclav Kotesovec, Apr 28 2014

From Colin Barker, Dec 20 2017: (Start)

G.f.: x*(1 - x + x^2) / ((1 - x)*(1 + x^4)).

a(n) = a(n-1) - a(n-4) + a(n-5) for n>4.

(End)