A206687 -id:A206687 - cp's OEIS frontend

A240893 T(n,k)=Number of nXk 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

1, 1, 1, 2, 4, 2, 4, 11, 11, 4, 8, 36, 57, 36, 8, 16, 116, 289, 289, 116, 16, 32, 376, 1485, 2362, 1485, 376, 32, 64, 1216, 7609, 19065, 19065, 7609, 1216, 64, 128, 3936, 38981, 154858, 245268, 154858, 38981, 3936, 128, 256, 12736, 199761, 1255585, 3146755

Offset: 1

R. H. Hardin, Apr 14 2014

Table starts
...1.....1.......2.........4...........8.............16...............32
...1.....4......11........36.........116............376.............1216
...2....11......57.......289........1485...........7609............38981
...4....36.....289......2362.......19065.........154858..........1255585
...8...116....1485.....19065......245268........3146755.........40424861
..16...376....7609....154858.....3146755.......64074526.......1302610899
..32..1216...38981...1255585....40424861.....1302610899......41971040844
..64..3936..199761..10186158...519218802....26501432610....1352138182759
.128.12736.1023597..82615013..6669141957...539075345618...43565815810587
.256.41216.5245049.670126562.85661208693.10966382557858.1403705064843757

			Some solutions for n=4 k=4
..0..1..2..1....0..1..2..0....0..1..1..0....0..1..2..1....0..1..2..0
..1..2..1..0....2..0..0..1....2..1..1..2....2..0..1..2....1..2..0..2
..2..1..0..2....1..0..0..2....1..0..0..1....1..2..0..1....0..0..2..1
..1..2..1..0....2..1..2..0....2..0..0..2....0..1..2..0....0..0..1..2

R. H. Hardin, Table of n, a(n) for n = 1..180

Column 1 is A000079(n-2)

Column 2 is A206687

Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>2
k=2: a(n) = 2*a(n-1) +4*a(n-2) for n>4
k=3: a(n) = 3*a(n-1) +8*a(n-2) +14*a(n-3) +4*a(n-4)
k=4: [order 16]
k=5: [order 48]

A241108 T(n,k)=Number of nXk 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

1, 1, 1, 2, 4, 2, 4, 11, 11, 4, 8, 36, 58, 36, 8, 16, 116, 294, 294, 116, 16, 32, 376, 1522, 2436, 1522, 376, 32, 64, 1216, 7846, 19814, 19814, 7846, 1216, 64, 128, 3936, 40418, 162776, 259388, 162776, 40418, 3936, 128, 256, 12736, 208374, 1333934, 3374086

Offset: 1

R. H. Hardin, Apr 16 2014

Table starts
...1.....1.......2.........4...........8.............16...............32
...1.....4......11........36.........116............376.............1216
...2....11......58.......294........1522...........7846............40418
...4....36.....294......2436.......19814.........162776..........1333934
...8...116....1522.....19814......259388........3374086.........44030862
..16...376....7846....162776.....3374086.......70145916.......1454236806
..32..1216...40418...1333934....44030862.....1454236806......48054344508
..64..3936..208374..10937316...574246744....30189380016....1586763763374
.128.12736.1074002..89651534..7489718098...626548445696...52415988665902
.256.41216.5535686.734979136.97685897406.13004327687556.1731396543937826

			Some solutions for n=4 k=4
..0..1..1..2....0..1..1..2....0..1..2..0....0..1..0..2....0..1..2..0
..2..1..1..0....2..1..1..1....1..2..1..2....1..0..2..1....1..0..0..2
..1..0..2..1....0..2..1..1....2..1..2..0....2..1..1..0....2..0..0..0
..0..2..0..2....2..0..2..0....1..2..0..2....0..1..1..2....1..2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..144

Column 1 is A000079(n-2)

Column 2 is A206687

Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>2
k=2: a(n) = 2*a(n-1) +4*a(n-2) for n>4
k=3: a(n) = 3*a(n-1) +8*a(n-2) +16*a(n-3)
k=4: [order 10]
k=5: [order 26]
k=6: [order 76]

cp's OEIS Frontend

A240893 T(n,k)=Number of nXk 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula