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!)
A333651 Triangle T(n,k), n >= 2, 0 <= k <= floor(n^2/2)-2, read by rows, where T(n,k) is the number of 2*(k+2)-cycles in the n X n grid graph which pass through NW corner (0,0). 4
1, 1, 2, 4, 1, 2, 6, 18, 40, 24, 6, 1, 2, 6, 20, 72, 248, 698, 1100, 1096, 662, 206, 1, 2, 6, 20, 74, 298, 1228, 4762, 15984, 40026, 75524, 109150, 121130, 99032, 51964, 11996, 1072, 1, 2, 6, 20, 74, 300, 1300, 5844, 26148, 110942, 427388, 1393796, 3790524, 8648638, 16727776, 27529284, 38120312, 43012614, 37385280, 23166526, 9496426, 2286972, 242764 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
LINKS
Seiichi Manyama, Rows n = 2..9, flattened
FORMULA
T(n,k) = A034010(k+2) for k <= n-2.
EXAMPLE
T(3,0) = 1;
+--*
| |
*--*
T(3,1) = 2;
+--*--* +--*
| | | |
*--*--* * *
| |
*--*
T(3,2) = 4;
+--*--* +--*--* +--*--* +--*
| | | | | | | |
* * * *--* *--* * * *--*
| | | | | | | |
*--*--* *--* *--* *--*--*
Triangle starts:
===================================================
n\k| 0 1 2 3 4 5 6 ... 10 ... 16
---|-----------------------------------------------
2 | 1;
3 | 1, 2, 4;
4 | 1, 2, 6, 18, 40, 24, 6;
5 | 1, 2, 6, 20, 72, 248, 698, ... , 206;
6 | 1, 2, 6, 20, 74, 298, 1228, .......... , 1072;
7 | 1, 2, 6, 20, 74, 300, 1300, ...
8 | 1, 2, 6, 20, 74, 300, 1302, ...
9 | 1, 2, 6, 20, 74, 300, 1302, ...
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333651(n):
universe = tl.grid(n - 1, n - 1)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles().including(1)
return [cycles.len(2 * k).len() for k in range(2, n * n // 2 + 1)]
print([i for n in range(2, 8) for i in A333651(n)])
CROSSREFS
Row sums give A333246.
Sequence in context: A194671 A331696 A364837 * A131398 A249307 A209581
KEYWORD
nonn,tabf
AUTHOR
Seiichi Manyama, Apr 01 2020
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 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)