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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A100692 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

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Last modified June 27 00:08 EDT 2022. Contains 354888 sequences. (Running on oeis4.)