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A333571
Square array T(n,k), n >= 1, k >= 2, read by antidiagonals, where T(n,k) is the number of Hamiltonian paths in the n X k grid graph which start at any of the n vertices on left side of the graph and terminate at any of the n vertices on the right side.
3
1, 1, 2, 1, 2, 4, 1, 2, 8, 6, 1, 2, 16, 14, 10, 1, 2, 32, 34, 38, 14, 1, 2, 64, 80, 162, 74, 20, 1, 2, 128, 190, 650, 426, 170, 26, 1, 2, 256, 450, 2728, 2166, 1594, 338, 34, 1, 2, 512, 1066, 11250, 12014, 12908, 4374, 724, 42, 1, 2, 1024, 2526, 46984, 62714, 119364, 47738, 14640, 1448, 52
OFFSET
1,3
LINKS
EXAMPLE
Square array T(n,k) begins:
1, 1, 1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, 2, 2, ...
4, 8, 16, 32, 64, 128, 256, ...
6, 14, 34, 80, 190, 450, 1066, ...
10, 38, 162, 650, 2728, 11250, 46984, ...
14, 74, 426, 2166, 12014, 62714, 340510, ...
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A(start, goal, n, k):
universe = tl.grid(n - 1, k - 1)
GraphSet.set_universe(universe)
paths = GraphSet.paths(start, goal, is_hamilton=True)
return paths.len()
def A333571(n, k):
if n == 1: return 1
s = 0
for i in range(1, n + 1):
for j in range(k * n - n + 1, k * n + 1):
s += A(i, j, k, n)
return s
print([A333571(j + 1, i - j + 2) for i in range(11) for j in range(i + 1)])
CROSSREFS
Columns k=2-3 give: A333574, A333575.
Rows n=1-3 give: A000012, 2*A000012, A000079.
T(n,n) gives A121789(n-1).
Cf. A333509.
Sequence in context: A226441 A080246 A113413 * A125694 A136678 A110162
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Mar 27 2020
STATUS
approved