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!)
A059268 Concatenate subsequences [2^0, 2^1, ..., 2^n] for n = 0, 1, 2, ... 24
1, 1, 2, 1, 2, 4, 1, 2, 4, 8, 1, 2, 4, 8, 16, 1, 2, 4, 8, 16, 32, 1, 2, 4, 8, 16, 32, 64, 1, 2, 4, 8, 16, 32, 64, 128, 1, 2, 4, 8, 16, 32, 64, 128, 256, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Triangular array T(n,k) read by rows, where T(n,k) = i!*j! times coefficient of x^n*y^k in exp(x+2y).
a(n) = A018900(n+1) - A140513(n). - Reinhard Zumkeller, Jun 24 2009
T(n,k) = A173786(n-1,k-1) - A173787(n-1,k-1), 0<k<=n. - Reinhard Zumkeller, Feb 28 2010
T(n,k) is the number of subsets of {0,1,...,n} whose largest element is k. To see this, let A be any subset of the 2^k subsets of {0,1,...,k-1}. Then there are 2^k subsets of the form (A U {k}). See example below. - Dennis P. Walsh, Nov 27 2011
Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements. A059268 is reluctant sequence of sequence A000079. - Boris Putievskiy, Dec 17 2012
LINKS
Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.
FORMULA
E.g.f.: exp(x+2*y) (T coordinates).
T(n,k) = 2^k. - Reinhard Zumkeller, Jan 29 2010
As a linear array, the sequence is a(n) = 2^((n-1-t(t+1)/2), where t = floor((-1+sqrt(8*n-7))/2), n>=1. - Boris Putievskiy, Dec 17 2012
As a linear array, the sequence is a(n) = 2^((n-1-t(t+1)/2), where t = floor(sqrt(2*n)-1/2), n>=1. - Zhining Yang, Jun 09 2017
EXAMPLE
T(4,3)=8 since there are 8 subsets of {0,1,2,3,4} whose largest element is 3, namely, {3}, {0,3}, {1,3}, {2,3}, {0,1,3}, {0,2,3}, {1,2,3}, and {0,1,2,3}.
Triangle starts:
1;
1, 2;
1, 2, 4;
1, 2, 4, 8;
1, 2, 4, 8, 16;
1, 2, 4, 8, 16, 32;
...
MAPLE
seq(seq(2^k, k=0..n), n=0..10);
MATHEMATICA
Table[2^k, {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 10 2013 *)
PROG
(Haskell)
a059268 n k = a059268_tabl !! n !! k
a059268_row n = a059268_tabl !! n
a059268_tabl = iterate (scanl (+) 1) [1]
-- Reinhard Zumkeller, Apr 18 2013, Jul 05 2012
CROSSREFS
Cf. A140531.
Cf. A000079.
Cf. A131816.
Row sums give A126646.
Sequence in context: A059250 A303696 A131074 * A300653 A256009 A123937
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jan 23 2001
EXTENSIONS
Formula corrected by Reinhard Zumkeller, Feb 23 2010
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 June 25 16:46 EDT 2024. Contains 373705 sequences. (Running on oeis4.)