A288033
Number of (undirected) paths in the n X n king graph.
Original entry on oeis.org
0, 30, 5148, 6014812, 57533191444, 4956907379126694, 3954100866385811897908, 29986588563791584765930866780, 2187482261973324160097873804506155572, 1550696105068168200375810546149511240714556526
Offset: 1
A288032
Number of (undirected) paths in the n X n grid graph.
Original entry on oeis.org
0, 12, 322, 14248, 1530196, 436619868, 343715004510, 766012555199052, 4914763477312679808, 91781780911712980966236, 5028368533802124263609489682, 813124448051069045700905179168520
Offset: 1
A343307
a(n) is the number of self-avoiding paths connecting consecutive corners of an n X n triangular grid.
Original entry on oeis.org
1, 2, 10, 108, 2726, 168724, 25637074, 9454069104, 8461610420420, 18438745892175008, 97929194419509169380, 1267379450261470833222676, 39964658780097197018058705552, 3071011528804416058638501563820092, 575150143830631835000028468717331605240
Offset: 1
For n = 3:
- we have the following paths:
. .
.
. . .
.
. o---o---o
.
.
. . . .
.
. o . o o . o
. / \ / \ / \ / \
. o o---o o o o o---o o
.
.
. . . .
.
. o---o o---o o---o
. / / / \ \ \
. o o---o o . o o---o o
.
.
. o o o
. / \ / \ / \
. o o o o o o
. / / / \ \ \
. o o---o o . o o---o o
- so a(3) = 10.
A308144
Number of (undirected) Hamiltonian paths on the triangular grid with n vertices on each side.
Original entry on oeis.org
1, 3, 12, 114, 1968, 66312, 4381020, 578266212, 153350225268, 82409298702462, 90180040305841212, 201800030110625440248, 926548406689594565864346, 8752381854153235620928637604
Offset: 1
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