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A057211 n-th run has length n. 12
1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Seen as a triangle read by rows: T(n,k) = n mod 2, 1<=k<=n. - Reinhard Zumkeller, Mar 18 2011

a(A007607(n)) = 0; a(A007606(n)) = 1. - Reinhard Zumkeller, Dec 30 2011

Row sums give A193356. - Omar E. Pol, Mar 05 2014

REFERENCES

K. H. Rosen, Discrete Mathematics and its Applications, 1999, Fourth Edition, page 79, exercise 10 (g).

LINKS

Reinhard Zumkeller, Rows n=1..125 of triangle, flattened

Index entries for characteristic functions

FORMULA

a(n) = (1-(-1)^A002024(n))/2, where A002024(n)=round(sqrt(2*n)). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 23 2003

Also a(n) = A000035(A002024(n)) = A002024(n) mod 2 = A002024(n)-2*floor(A002024(n)/2). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 23 2003

G.f.: x/(1-x)*sum_{n>=0} (-1)^n*x^(n*(n+1)/2). - Mircea Merca, Mar 05 2014

MAPLE

A002024 := n->round(sqrt(2*n)):A057211 := n->(1-(-1)^A002024(n))/2;

MATHEMATICA

Flatten[Table[{PadRight[{}, n, 1], PadRight[{}, n+1, 0]}, {n, 1, 21, 2}]] (* Harvey P. Dale, Jun 07 2015 *)

PROG

(Haskell)

a057211 n = a057211_list !! (n-1)

a057211_list = concat $ zipWith ($) (map replicate [1..]) a059841_list

-- Reinhard Zumkeller, Mar 18 2011

CROSSREFS

Cf. A057212.

Cf. A059841.

Sequence in context: A285083 A266982 A051341 * A120531 A106665 A004609

Adjacent sequences:  A057208 A057209 A057210 * A057212 A057213 A057214

KEYWORD

nonn,tabl

AUTHOR

Ben Tyner (tyner(AT)phys.ufl.edu), Sep 27 2000

STATUS

approved

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Last modified July 31 06:15 EDT 2021. Contains 346369 sequences. (Running on oeis4.)