A140513 Repeat 2^n n times.

2, 4, 4, 8, 8, 8, 16, 16, 16, 16, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 128, 128, 128, 128, 128, 128, 128, 256, 256, 256, 256, 256, 256, 256, 256, 512, 512, 512, 512, 512, 512, 512, 512, 512, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024

Offset: 0

Author

Paul Curtz, Jul 01 2008

Keywords

• nonn
• tabl

Links

• Reinhard Zumkeller, Rows n = 0..127 of triangle, flattened
• Sajed Haque, Chapter 2.6.2 of Discriminators of Integer Sequences, 2017, See p. 34.

Crossrefs

Cf. A000079, A018900, A059268, A111650, A137688.

Programs

Haskell

a140513 n k = a140513_tabl !! (n-1) !! (k-1)
a140513_row n = a140513_tabl !! (n-1)
a140513_tabl = iterate (\xs@(x:_) -> map (* 2) (x:xs)) [2]
a140513_list = concat a140513_tabl
-- Reinhard Zumkeller, Nov 14 2015

Mathematica

t={}; Do[r={}; Do[If[k==0||k==n, m=2^n, m=t[[n, k]] + t[[n, k + 1]]]; r=AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t=Flatten[2 t] (* Vincenzo Librandi, Feb 17 2018 *)
Table[Table[2^n,n],{n,10}]//Flatten (* Harvey P. Dale, Dec 04 2018 *)

Python

from math import isqrt
def A140513(n): return 1<<(m:=isqrt(k:=n+1<<1))+(k>m*(m+1)) # Chai Wah Wu, Nov 07 2024

Formula

a(n) = 2*A137688(n).

a(n) = A018900(n+1) - A059268(n). - Reinhard Zumkeller, Jun 24 2009

From Reinhard Zumkeller, Feb 28 2010: (Start)

Seen as a triangle read by rows: T(n,k)=2^n, 1 <= k <= n.

T(n,k) = A173786(n-1,k-1) + A173787(n-1,k-1), 1 <= k <= n. (End)

Sum_{n>=0} 1/a(n) = 2. - Amiram Eldar, Aug 16 2022