login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A062111 Upper-right triangle resulting from binomial transform calculation for nonnegative integers. 10
0, 1, 1, 4, 3, 2, 12, 8, 5, 3, 32, 20, 12, 7, 4, 80, 48, 28, 16, 9, 5, 192, 112, 64, 36, 20, 11, 6, 448, 256, 144, 80, 44, 24, 13, 7, 1024, 576, 320, 176, 96, 52, 28, 15, 8, 2304, 1280, 704, 384, 208, 112, 60, 32, 17, 9, 5120, 2816, 1536, 832, 448, 240, 128, 68, 36, 19, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

From Philippe Deléham, Apr 15 2007 (Start)

This triangle can be found in the Laisant reference in the following form:

...............................5...11

..........................4...9...20

.....................3...7..16...36

................2...5..12..28.....

...........1...3...8..20..48.....

......0...1...4..12..32..80...... (End)

Triangle A152920 reversed . [Philippe Deléham, Apr 21 2009]

LINKS

Table of n, a(n) for n=0..65.

F. Ellermann, Illustration of binomial transforms

C.-A. Laisant, Sur les tableaux de sommes - Nouvelles applications, Compt. Rendus de l'Association Francaise pour l'Avancement des Sciences, Aout. 04, 1893, pp. 206-216 (table given on p. 212).

FORMULA

a(n, n) = n; a(n, k)=a(n, k-1)+a(n+1, k) if k>n. a(n, k)=(k+n)*2^(k-n-1) if k >= n.

T(2n,n) = 3*n*2^(n-1) = 3*A001787(n). [Philippe Deléham, Apr 21 2009]

EXAMPLE

Rows start (0,1,4,12,32,...), (1,3,8,20,...), (2,5,12,...), (3,7,...), etc.

CROSSREFS

Rows include (essentially) A001787, A001792, A045623, A045891, A034007. Diagonals include (essentially) A001477, A005408, A008586, A017113, A017113, A008598. Column sums are A058877.

Cf. A111297, A159694, A159695, A159696, A159697. [Philippe Deléham, Apr 21 2009]

Sequence in context: A227182 A065367 A033882 * A181596 A182142 A033881

Adjacent sequences:  A062108 A062109 A062110 * A062112 A062113 A062114

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, May 30 2001

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 19 06:47 EDT 2019. Contains 324218 sequences. (Running on oeis4.)