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A135528 1, then repeat 1,0. 6
1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is Guy Steele's sequence GS(2, 1) (see A135416).

2-adic expansion of 1/3 (right to left): 1/3 = ...01010101010101011. - Philippe Deléham, Mar 24 2009

Also, with offset 0, parity of A036467(n-1). - Omar E. Pol, Mar 17 2015

LINKS

Table of n, a(n) for n=1..105.

Andrei Asinowski, Cyril Banderier, Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, (2019).

FORMULA

a(n) = (1/2)*(1+(-1)^n)+(C(2*(n-1),(n-1)) mod 2). - Paolo P. Lava, Mar 03 2008

G.f.: x*(1+x-x^2)/(1-x^2). - Philippe Deléham, Feb 08 2012

G.f.: x / (1 - x / (1 + x / (1 + x / (1 - x)))). - Michael Somos, Apr 02 2012

a(n) = A049711(n+2) mod 2. - Ctibor O. Zizka, Jan 28 2019

EXAMPLE

G.f. = x + x^2 + x^4 + x^6 + x^8 + x^10 + x^12 + x^14 + x^16 + x^18 + x^20 + ...

MAPLE

GS(2, 1, 200); [see A135416].

MATHEMATICA

Prepend[Table[Mod[n + 1, 2], {n, 2, 60}], 1] (* Michael De Vlieger, Mar 17 2015 *)

PROG

(Haskell)

a135528 n = a135528_list !! (n-1)

a135528_list = concat $ iterate ([1, 0] *) [1]

instance Num a => Num [a] where

fromInteger k = [fromInteger k]

   (p:ps) + (q:qs) = p + q : ps + qs

   ps + qs         = ps ++ qs

   (0:ps) * qs         = 0 : ps * qs

   (p:ps) * qs'@(q:qs) = p * q : ps * qs' + [p] * qs

   _ * _               = []

-- Reinhard Zumkeller, Apr 02 2011

CROSSREFS

Cf. A036467, A049711, A135416.

Sequence in context: A257170 A073097 A117569 * A163805 A267015 A078387

Adjacent sequences:  A135525 A135526 A135527 * A135529 A135530 A135531

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, based on a message from Guy Steele and Don Knuth, Mar 01 2008

STATUS

approved

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Last modified June 26 09:52 EDT 2022. Contains 354879 sequences. (Running on oeis4.)