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!)
A209919 Triangle read by rows: T(n,k), 0 <= k <= n-1, = number of 2-divided binary sequences of length n which are 2-divisible in exactly k ways. 3
0, 3, 1, 4, 2, 2, 6, 3, 4, 3, 8, 6, 6, 6, 6, 14, 9, 11, 10, 11, 9, 20, 18, 18, 18, 18, 18, 18, 36, 30, 33, 30, 34, 30, 33, 30, 60, 56, 56, 58, 56, 56, 58, 56, 56, 108, 99, 105, 99, 105, 100, 105, 99, 105, 99, 188, 186, 186, 186, 186, 186, 186, 186, 186, 186, 186, 352, 335, 344, 338, 346, 335, 348, 335, 346, 338, 344, 335, 632, 630, 630, 630, 630, 630, 630, 630, 630, 630, 630, 630, 630, 1182, 1161, 1179, 1161, 1179, 1161, 1179, 1162, 1179, 1161, 1179, 1161, 1179, 1161, 2192, 2182, 2182, 2188, 2182, 2184, 2188, 2182, 2182, 2188, 2184, 2182, 2188, 2182, 2182 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Computed by David Scambler.
See A210109 for further information.
Omitting the leading column, triangle has mirror symmetry.
Speculation: T(2n+1,2)=T(2n+1,1); T(2n,2)=T(2n,1)+T(n,1); T(3n+1,3)=T(3n+1,1); T(3n+2,3)=T(3n+2,1); T(3n,3)=T(3n,1)+T(n,1) and similar "lagged modulo sums" for T(4n+i,4)=T(4n+i,2), 0<i<=3; T(4n,4)=T(4n,2)+T(n,1); T(5n+i,5)=T(5n+i,1), 0<i<=4; T(5n,5)=T(5n,1)+T(n,1). - R. J. Mathar, Mar 27 2012
Right border appears to be A059966. - Michel Marcus, Apr 26 2013
LINKS
EXAMPLE
Triangle begins:
n k=0 k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9 k=10 k=11 k=12 k=13 k=14
1 1
2 3 1
3 4 2 2
4 6 3 4 3
5 8 6 6 6 6
6 14 9 11 10 11 9
7 20 18 18 18 18 18 18
8 36 30 33 30 34 30 33 30
9 60 56 56 58 56 56 58 56 56
10 108 99 105 99 105 100 105 99 105 99
11 188 186 186 186 186 186 186 186 186 186 186
12 352 335 344 338 346 335 348 335 346 338 344 335
13 632 630 630 630 630 630 630 630 630 630 630 630 630
14 1182 1161 1179 1161 1179 1161 1179 1162 1179 1161 1179 1161 1179 1161
15 2192 2182 2182 2188 2182 2184 2188 2182 2182 2188 2184 2182 2188 2182 2182...
CROSSREFS
First column is A000031, second column is conjectured to be A001037. Row sums = 2^n.
Sequence in context: A237016 A135822 A242111 * A116537 A194307 A346770
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Mar 21 2012
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 March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)