A339118
Number of cycles in the grid graph P_6 X P_n.
Original entry on oeis.org
15, 275, 5034, 80626, 1222363, 18438929, 279285399, 4237530095, 64300829449, 975566486675, 14800469958185, 224540402345213, 3406558215857382, 51681816786790684, 784078741397570677, 11895467318139343215, 180469294422664219486, 2737947622842077799930
Offset: 2
-
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A(n, k):
universe = tl.grid(n - 1, k - 1)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
def A339118(n):
return A(6, n)
print([A339118(n) for n in range(2, 13)])
A339119
Number of cycles in the grid graph P_7 X P_n.
Original entry on oeis.org
21, 681, 23984, 692194, 18438929, 487150371, 12947640143, 345142437669, 9203308475041, 245355064111139, 6540331954247241, 174341025325354201, 4647322411026104632, 123881845810609904802, 3302270967098053652763, 88027348826922694314763, 2346510376337057464408514
Offset: 2
-
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A(n, k):
universe = tl.grid(n - 1, k - 1)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
def A339119(n):
return A(n, 7)
print([A339119(n) for n in range(2, 15)])
A339120
Number of cycles in the grid graph P_8 X P_n.
Original entry on oeis.org
28, 1664, 114069, 5948291, 279285399, 12947640143, 603841648931, 28251882697663, 1322310119854705, 61875355046353061, 2895006802805407868, 135448608195945754204, 6337277838067727854392, 296505504331623399871908, 13872765058478362509835979, 649072483984291902586660423
Offset: 2
A339121
Number of cycles in the grid graph P_9 X P_n.
Original entry on oeis.org
36, 4040, 542295, 51139577, 4237530095, 345142437669, 28251882697663, 2318527339461265, 190273063549680295, 15609156135669687673, 1280305089790914190288, 105011610206669201362004, 8613171107463963712000106, 706463610718638922253288622, 57945052730138702492774189915
Offset: 2
-
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A(n, k):
universe = tl.grid(n - 1, k - 1)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
def A339121(n):
return A(n, 9)
print([A339121(n) for n in range(2, 15)])
A271802
Number of cuttings of an n X n checkerboard along grid lines into two pieces with holes disallowed.
Original entry on oeis.org
0, 6, 52, 614, 16000, 1114394, 220762028, 127074234622, 215163221802400, 1080509693050320314, 16181730102294154610684, 725449589191165593072311582, 97631783799192329642727718567824, 39528641527526180063041016094650084850
Offset: 1
-
A068416 = Cases[Import["https://oeis.org/A068416/b068416.txt", "Table"], {, }][[All, 2]];
A140517 = Cases[Import["https://oeis.org/A140517/b140517.txt", "Table"], {, }][[All, 2]];
a[n_] := If[n == 1, 0, A068416[[n]] - A140517[[n - 1]]];
Array[a, 14] (* Jean-François Alcover, Sep 15 2019 *)
A358707
Number of cycles in the grid graph P_10 X P_n.
Original entry on oeis.org
45, 9779, 2577870, 439673502, 64300829449, 9203308475041, 1322310119854705, 190273063549680295, 27359264067916806101, 3931128009418993765997, 564680431992866012642342, 81106350080343571152166324, 11649258590678717543578165244, 1673159830616398545304368383554
Offset: 2
A368657
Number of cycles in an n X n grid where the cycle cannot touch itself orthogonally or diagonally and must contain at least one inside point.
Original entry on oeis.org
0, 0, 1, 13, 167, 2685, 50391, 1188935, 41749885, 2645126227, 341643017303, 82472721488013, 31312529515504513, 17381378412860375479, 14419291783372365769995, 18997663191047558313462721
Offset: 1
For n = 4, there are 13 valid cycles:
.
1 2 3 4
###. .### .... ....
#.#. .#.# .### ###.
###. .### .#.# #.#.
.... .... .### ###.
.
5 6 7 8
#### .... ###. .###
#..# #### #.#. .#.#
#### #..# #.#. .#.#
.... #### ###. .###
.
9 10 11 12
.### ###. #### ####
##.# #.## #..# #..#
#..# #..# #.## ##.#
#### #### ###. .###
.
13
####
#..#
#..#
####
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