A152822 - OEIS

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A152822

Periodic sequence [1,1,0,1] of length 4.

1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,1`
	LINKS	`Table of n, a(n) for n=0..104.` `Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).`
	FORMULA	`a(n) = 3/4 - (1/4)(-1)^n + (1/2)cos(nPi/2);` `a(n+4) = a(n) with a(0) = a(1) = a(3) = 1 and a(2) = 0;` `O.g.f.: (1+z+z^3)/(1-z^4);` `From Paolo P. Lava, Dec 15 2008: (Start)` `a(n) = (1/8)((n mod 4) - ((n+1) mod 4) + 3((n+2) mod 4)((n+3) mod 4)), with n >= 0.` `a(n) = (1/4)(3 + i^n + (-i)^n - (-1)^n), with n >= 0 and i = sqrt(-1). (End)` `a(n) = ceiling(cos(Pi*n/4)^2). - Wesley Ivan Hurt, Jun 12 2013`
	PROG	`(PARI) a(n)=n%4!=2 \\ Jaume Oliver Lafont, Mar 24 2009`
	CROSSREFS	`Cf. A026052, A026064.` `Sequence in context: A085369 A188082 A046980 * A118831 A118828 A105234` `Adjacent sequences: A152819 A152820 A152821 * A152823 A152824 A152825`
	KEYWORD	`easy,nonn,mult`
	AUTHOR	`Richard Choulet, Dec 13 2008`
	EXTENSIONS	`More terms from Philippe Deléham, Dec 21 2008` `Keyword:mult added by Andrew Howroyd, Jul 27 2018`
	STATUS	`approved`

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Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)