A265887 T(n,k)=Number of nXk 0..2 arrays with the sum of the absolute differences of each element with its horizontal and vertical neighbors equal to the number of neighbors.

3, 4, 4, 6, 12, 6, 8, 16, 16, 8, 12, 32, 68, 32, 12, 16, 64, 128, 128, 64, 16, 24, 128, 384, 664, 384, 128, 24, 32, 256, 1024, 2048, 2048, 1024, 256, 32, 48, 512, 3072, 8192, 13672, 8192, 3072, 512, 48, 64, 1024, 8192, 32768, 65536, 65536, 32768, 8192, 1024, 64, 96

Offset

1,1

Comments

Table starts

..3....4.....6.......8.......12.........16..........24............32

..4...12....16......32.......64........128.........256...........512

..6...16....68.....128......384.......1024........3072..........8192

..8...32...128.....664.....2048.......8192.......32768........131072

.12...64...384....2048....13672......65536......393216.......2097152

.16..128..1024....8192....65536.....560512.....4194304......33554432

.24..256..3072...32768...393216....4194304....51483264.....536870912

.32..512..8192..131072..2097152...33554432...536870912....8726974464

.48.1024.24576..524288.12582912..268435456..6442450944..137438953472

.64.2048.65536.2097152.67108864.2147483648.68719476736.2199023255552

Links

R. H. Hardin, Table of n, a(n) for n = 1..684

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-2)

k=2: a(n) = 2*a(n-1) for n>3

k=3: a(n) = 8*a(n-2) for n>5

k=4: a(n) = 4*a(n-1) for n>5

k=5: a(n) = 32*a(n-2) for n>7

k=6: a(n) = 8*a(n-1) for n>7

k=7: a(n) = 128*a(n-2) for n>9

Example

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

Crossrefs

Column 1 is A029744(n+2).

Sequence in context: A360724 A089640 A086659 * A345264 A344465 A008473

Adjacent sequences: A265884 A265885 A265886 * A265888 A265889 A265890

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 17 2015

Status

approved