A143246
Number of (directed) Hamiltonian circuits in the n X n grid graph.
Original entry on oeis.org
0, 2, 0, 12, 0, 2144, 0, 9277152, 0, 934520913216, 0, 2152453777211211412, 0, 112252999240982874562527216, 0, 131765033045251672652319572331061144, 0, 3467852755777932367855581588111341658695967892, 0
Offset: 1
Cf.
A003763 (number of undirected cycles on 2n X 2n grid graph).
A238115
Number of states arising in matrix method for enumerating Hamiltonian cycles on a 2n X 2n grid.
Original entry on oeis.org
1, 6, 32, 182, 1117, 7280, 49625, 349998, 2535077, 18758264, 141254654, 1079364104, 8350678169, 65298467486, 515349097712, 4100346740510, 32858696386765, 265001681344568, 2149447880547398, 17524254766905368, 143540915998174577, 1180736721910617182
Offset: 1
-
a := n -> hypergeom([1/2, -n, -n], [1, 2], 4) - 1:
seq(simplify(a(n)), n = 1..22); # Peter Luschny, Dec 13 2024
-
a(n)=sum(k=1,n,binomial(n,k)^2*binomial(2*k,k)/(k+1)) \\ Andrew Howroyd, Dec 13 2024
A238116
Number of continuations arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.
Original entry on oeis.org
1, 14, 162, 1966, 25567, 351880, 5056350, 75100735, 1144833705, 17821104101
Offset: 1
A238117
Number of states with reflective symmetry arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.
Original entry on oeis.org
1, 4, 14, 40, 120, 320, 946, 2496, 7418, 19616
Offset: 1
A238118
Number of continuations with reflective symmetry arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.
Original entry on oeis.org
1, 6, 20, 101, 327, 1560, 5333, 24727, 88422, 403552
Offset: 1
Showing 1-5 of 5 results.