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A165211 Period 8: repeat 0,1,0,1,1,0,1,0. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

FORMULA

a(n) = (1/56)*((n mod 8) + 8*((n+1) mod 8) - 6*((n+2) mod 8) + 8*((n+3) mod 8) + ((n+4) mod 8) - 6*((n+5) mod 8) + 8*((n+6) mod 8) - 6*((n+7) mod 8)), with n >= 0. - Paolo P. Lava, Sep 16 2009

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)

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 *)

PROG

(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

CROSSREFS

Sequence in context: A285249 A269027 A089809 * A188027 A193496 A284533

Adjacent sequences:  A165208 A165209 A165210 * A165212 A165213 A165214

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Sep 07 2009

STATUS

approved

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Last modified January 21 18:06 EST 2019. Contains 319349 sequences. (Running on oeis4.)