cp's OEIS Frontend

A333602 Number of directed Hamiltonian walks from NW to SW corners of a 6 X n grid.

%I A333602 #30 Feb 22 2022 00:32:37
%S A333602 1,1,16,47,397,1770,11658,59946,359962,1958968,11341696,63142224,
%T A333602 360314940,2024278172,11485023624,64758162416,366573071464,
%U A333602 2069908196378,11706322628832,66139560111600,373914808423830,2113066820134474,11944325099736622,67505931650135578
%N A333602 Number of directed Hamiltonian walks from NW to SW corners of a 6 X n grid.
%H A333602 Andrew Howroyd, <a href="/A333602/b333602.txt">Table of n, a(n) for n = 1..500</a>
%H A333602 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (5,14,-63,12,90,-35,-66,118,-8,-82,42,28,-4,2).
%F A333602 a(n) = 5*a(n-1) + 14*a(n-2) - 63*a(n-3) + 12*a(n-4) + 90*a(n-5) - 35*a(n-6) - 66*a(n-7) + 118*a(n-8) - 8*a(n-9) - 82*a(n-10) + 42*a(n-11) + 28*a(n-12) - 4*a(n-13) + 2*a(n-14), n > 14. - _Michael Gray_, Jan 30 2022
%F A333602 G.f.: x*(1 - x)*(1 - 3*x - 6*x^2 + 10*x^3 - x^4 + 32*x^5 - 4*x^6 - 20*x^7 + 24*x^8 + 13*x^9 + 2*x^10 + 2*x^11)/(1 - 5*x - 14*x^2 + 63*x^3 - 12*x^4 - 90*x^5 + 35*x^6 + 66*x^7 - 118*x^8 + 8*x^9 + 82*x^10 - 42*x^11 - 28*x^12 + 4*x^13 - 2*x^14). - _Andrew Howroyd_, Jan 31 2022
%o A333602 (Python)
%o A333602 # Using graphillion
%o A333602 from graphillion import GraphSet
%o A333602 import graphillion.tutorial as tl
%o A333602 def A271592(n, k):
%o A333602     if k == 1: return 1
%o A333602     universe = tl.grid(k - 1, n - 1)
%o A333602     GraphSet.set_universe(universe)
%o A333602     start, goal = 1, n
%o A333602     paths = GraphSet.paths(start, goal, is_hamilton=True)
%o A333602     return paths.len()
%o A333602 def A333602(n):
%o A333602     return A271592(6, n)
%o A333602 print([A333602(n) for n in range(1, 10)])
%Y A333602 Row n=6 of A271592.
%Y A333602 Cf. A333581.
%K A333602 nonn,easy,walk
%O A333602 1,3
%A A333602 _Seiichi Manyama_, Mar 28 2020
%E A333602 a(20)-a(24) from _Michael Gray_, Jan 31 2022