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

%I A333603 #14 Mar 13 2023 16:21:59
%S A333603 1,32,1584,88418,4999752,283163450,16039767268,908585449166,
%T A333603 51467614908516,2915428131919456,165146980589118258,
%U A333603 9354895388703582168,529916244425510621368,30017569886372177468776,1700371542421991554910438,96319035592388073867700014,5456076149237165677047910650
%N A333603 Number of directed Hamiltonian walks from NW to SW corners of a 7 X (2*n+1) grid.
%H A333603 Seiichi Manyama, <a href="/A333603/b333603.txt">Table of n, a(n) for n = 0..500</a>
%F A333603 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
%o A333603 (Python)
%o A333603 # Using graphillion
%o A333603 from graphillion import GraphSet
%o A333603 import graphillion.tutorial as tl
%o A333603 def A271592(n, k):
%o A333603     if k == 1: return 1
%o A333603     universe = tl.grid(k - 1, n - 1)
%o A333603     GraphSet.set_universe(universe)
%o A333603     start, goal = 1, n
%o A333603     paths = GraphSet.paths(start, goal, is_hamilton=True)
%o A333603     return paths.len()
%o A333603 def A333603(n):
%o A333603     return A271592(7, 2 * n + 1)
%o A333603 print([A333603(n) for n in range(20)])
%Y A333603 Row n=7 of A271592 (with 0 omitted).
%Y A333603 Cf. A333582.
%K A333603 nonn
%O A333603 0,2
%A A333603 _Seiichi Manyama_, Mar 28 2020