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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 (list; table; graph; refs; listen; history; text; internal format)
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 * A128409 A133699 A157361

Adjacent sequences:  A271589 A271590 A271591 * A271593 A271594 A271595

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Apr 10 2016

STATUS

approved

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Last modified November 27 23:47 EST 2020. Contains 338685 sequences. (Running on oeis4.)