

A271592


Array read by antidiagonals: T(n,m) = number of directed Hamiltonian walks from NW to SW corners on a grid with n rows and m columns.


15



1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 4, 0, 1, 0, 1, 4, 8, 8, 1, 1, 0, 1, 0, 23, 0, 16, 0, 1, 0, 1, 8, 55, 86, 47, 32, 1, 1, 0, 1, 0, 144, 0, 397, 0, 64, 0, 1, 0, 1, 16, 360, 948, 1770, 1584, 264, 128, 1, 1, 0, 1, 0, 921, 0, 11658, 0, 6820, 0, 256, 0, 1
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OFFSET

1,13


LINKS

Andrew Howroyd, Antidiagonals n = 1..27, flattened


FORMULA

T(n,m)=0 for n odd and m even, T(1,n)=0 for n>1.
T(2,n)=T(n,1)=T(2*n,2)=1, T(3,2*n+1)=T(n+1,3)=2^n.


EXAMPLE

The start of the sequence as table:
* 1 0 0 0 0 0 0 0 0 ...
* 1 1 1 1 1 1 1 1 1 ...
* 1 0 2 0 4 0 8 0 16 ...
* 1 1 4 8 23 55 144 360 921 ...
* 1 0 8 0 86 0 948 0 10444 ...
* 1 1 16 47 397 1770 11658 59946 359962 ...
* 1 0 32 0 1584 0 88418 0 4999752 ...
* 1 1 64 264 6820 52387 909009 8934966 130373192 ...
* 1 0 128 0 28002 0 7503654 0 2087813834 ...
* ...


PROG

(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A271592(n, k):
if k == 1: return 1
universe = tl.grid(k  1, n  1)
GraphSet.set_universe(universe)
start, goal = 1, n
paths = GraphSet.paths(start, goal, is_hamilton=True)
return paths.len()
print([A271592(j + 1, i  j + 1) for i in range(12) for j in range(i + 1)]) # Seiichi Manyama, Mar 28 2020


CROSSREFS

Column 4 is aerated A014524, column 5 is A014585.
Rows include A181688, A181689.
Main diagonal is A000532.
Cf. A333580.
Sequence in context: A035155 A090584 A171400 * A357187 A128409 A133699
Adjacent sequences: A271589 A271590 A271591 * A271593 A271594 A271595


KEYWORD

nonn,tabl


AUTHOR

Andrew Howroyd, Apr 10 2016


STATUS

approved



