login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057211 Alternating runs of ones and zeros, where the 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

a(n) = 1 - A057212(n). - Alois P. Heinz, Oct 06 2021

MAPLE

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

# alternative Maple program:

T:= n-> [irem(n, 2)$n][]:

seq(T(n), n=1..14);  # Alois P. Heinz, Oct 06 2021

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, 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

EXTENSIONS

Definition amended by Georg Fischer, Oct 06 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 6 21:32 EDT 2022. Contains 357270 sequences. (Running on oeis4.)