A221024 T(n,k)=Equals one maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal, vertical and antidiagonal neighbors in a random 0..3 nXk array

1, 2, 2, 4, 8, 4, 8, 38, 38, 8, 16, 168, 371, 168, 16, 32, 726, 3474, 3474, 726, 32, 64, 3088, 30167, 62944, 30167, 3088, 64, 128, 12974, 251674, 1038208, 1038208, 251674, 12974, 128, 256, 54000, 2055232, 16735744, 33512960, 16735744, 2055232, 54000, 256, 512

Offset

1,2

Comments

Table starts

...1......2........4.........8.........16.........32..........64........128

...2......8.......38.......168........726.......3088.......12974......54000

...4.....38......371......3474......30167.....251674.....2055232...16609480

...8....168.....3474.....62944....1038208...16735744...268269568.4294303744

..16....726....30167...1038208...33512960.1073575936.34359074816

..32...3088...251674..16735744.1073575936

..64..12974..2055232.268269568

.128..54000.16609480

.256.223118

.512

Links

R. H. Hardin, Table of n, a(n) for n = 1..60

Formula

Empirical for column k:

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

k=2: a(n) = 7*a(n-1) -11*a(n-2) -3*a(n-3) -4*a(n-4)

k=3: a(n) = 12*a(n-1) -30*a(n-2) -24*a(n-3) +63*a(n-4) +12*a(n-5) -32*a(n-6) for n>11

k=4: a(n) = 20*a(n-1) -64*a(n-2) for n>5

k=5: a(n) = 36*a(n-1) -128*a(n-2) for n>5

Example

Some solutions for n=3 k=4
..1..0..0..0....0..0..0..1....0..0..1..1....0..0..0..1....1..0..0..0
..0..1..0..0....0..0..1..0....0..0..0..0....0..1..0..0....0..1..1..0
..1..1..1..1....0..1..0..0....0..0..1..0....0..0..1..1....0..0..0..0

Crossrefs

Column 1 is A000079(n-1)

Column 2 is A220806

Sequence in context: A222659 A116694 A220810 * A220545 A220751 A220967

Adjacent sequences: A221021 A221022 A221023 * A221025 A221026 A221027

Keyword

nonn,tabl

Author

R. H. Hardin Dec 28 2012

Status

approved