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A101688 Once 1, once 0, repeat, twice 1, twice 0, repeat, thrice 1, thrice 0... and so on. 15
1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 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, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Triangle T read by rows: T(k,n) = 1 if n >= ceiling(k/2), 0 otherwise.

Square array A, read by antidiagonals upwards: A(k,n) = 1 if n >= k, 0 otherwise.

Partitions of n into k parts of size 1 or 2. - Nicolae Boicu, Aug 23 2018

LINKS

Table of n, a(n) for n=0..101.

Boris Putievskiy, Transformations (of) Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

FORMULA

G.f.: 1/[(1-xy)(1-y)]. k-th row of array: x^(k-1)/(1-x).

T(n, k) = if(binomial(k, n-k)>0, 1, 0). - Paul Barry, Aug 23 2005

From Boris Putievskiy, Jan 09 2013: (Start)

a(n) = floor((2*A002260(n)+1)/A003056(n)+3).

a(n) = floor((2*n-t*(t+1)+1)/(t+3)), where

t = floor((-1+sqrt(8*n-7))/2). (End)

a(n) = floor(sqrt(2*n+1)) - floor(sqrt(2*n+2) - 1/2). - Ridouane Oudra, Jul 16 2020

EXAMPLE

.1 1 1 1 1 1 1 1 1 ......... 1

.0 1 1 1 1 1 1 1 1 ........ 0 1

.0 0 1 1 1 1 1 1 1 ....... 0 1 1

.0 0 0 1 1 1 1 1 1 ...... 0 0 1 1

.0 0 0 0 1 1 1 1 1 ..... 0 0 1 1 1

.0 0 0 0 0 1 1 1 1 .... 0 0 0 1 1 1

.0 0 0 0 0 0 1 1 1 ... 0 0 0 1 1 1 1

.0 0 0 0 0 0 0 1 1 .. 0 0 0 0 1 1 1 1

.0 0 0 0 0 0 0 0 1 . 0 0 0 0 1 1 1 1 1

MATHEMATICA

rows = 15; A = Array[If[#1 <= #2, 1, 0]&, {rows, rows}]; Table[A[[i-j+1, j]], {i, 1, rows}, {j, 1, i}] // Flatten (* Jean-Fran├žois Alcover, May 04 2017 *)

CROSSREFS

Row/antidiagonal sums are A008619. Cf. A079813.

Sequence in context: A087748 A117446 A187034 * A155031 A155029 A134540

Adjacent sequences:  A101685 A101686 A101687 * A101689 A101690 A101691

KEYWORD

nonn,tabl

AUTHOR

Ralf Stephan, Dec 19 2004

STATUS

approved

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Last modified September 20 17:16 EDT 2020. Contains 337265 sequences. (Running on oeis4.)