A333603 Number of directed Hamiltonian walks from NW to SW corners of a 7 X (2*n+1) grid.

1, 32, 1584, 88418, 4999752, 283163450, 16039767268, 908585449166, 51467614908516, 2915428131919456, 165146980589118258, 9354895388703582168, 529916244425510621368, 30017569886372177468776, 1700371542421991554910438, 96319035592388073867700014, 5456076149237165677047910650

Offset: 0

Author

Seiichi Manyama, Mar 28 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Row n=7 of A271592 (with 0 omitted).

Cf. A333582.

Programs

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()
def A333603(n):
    return A271592(7, 2 * n + 1)
print([A333603(n) for n in range(20)])

Formula

Conjecture: a(n)= 85*a(n-1) -1932*a(n-2) +20403*a(n-3) -116734*a(n-4) +386724*a(n-5) -815141*a(n-6) +1251439*a(n-7) -1690670*a(n-8) +2681994*a(n-9) -4008954*a(n-10) +3390877*a(n-11) -1036420*a(n-12) -178842*a(n-13) +92790*a(n-14) +17732*a(n-15) -5972*a(n-16) +1728*a(n-17) +144*a(n-18). - R. J. Mathar, Mar 13 2023