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A333667
Triangle T(n,k), n >= 2, 0 <= k <= floor(n^2/2)-2*n+2, read by rows, where T(n,k) is the number of 2*(k+2*n-2)-cycles in the n X n grid graph which pass through NW and SE corners ((0,0),(n-1,n-1)).
4
1, 3, 20, 16, 6, 175, 420, 562, 456, 186, 1764, 8064, 21224, 39500, 55376, 57248, 37586, 10260, 1072, 19404, 138600, 569768, 1717152, 4151965, 8371428, 14126846, 19364732, 20241450, 14759356, 6998166, 1927724, 230440
OFFSET
2,2
LINKS
Seiichi Manyama, Rows n = 2..9, flattened
FORMULA
T(n,0) = A000891(n-2).
EXAMPLE
T(3,0) = 3;
+--*--* +--*--* +--*
| | | | | |
*--* * * * * *--*
| | | | | |
*--+ *--*--+ *--*--+
Triangle starts:
=======================================================================
n\k| 0 1 2 ... 4 ... 8 ... 12 ... 18
---|-------------------------------------------------------------------
2 | 1;
3 | 3;
4 | 20, 16, 6;
5 | 175, 420, 562, ... , 186;
6 | 1764, 8064, 21224, .......... , 1072;
7 | 19404, 138600, 569768, .................. , 230440;
8 | 226512, 2265120, 12922446, ............................ , 4638576;
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333667(n):
universe = tl.grid(n - 1, n - 1)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles().including(1).including(n * n)
return [cycles.len(2 * k).len() for k in range(2 * n - 2, n * n // 2 + 1)]
print([i for n in range(2, 8) for i in A333667(n)])
CROSSREFS
Row sums give A333323.
Sequence in context: A115280 A212995 A081849 * A375618 A169642 A222482
KEYWORD
nonn,tabf
AUTHOR
Seiichi Manyama, Apr 01 2020
STATUS
approved