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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 4
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 06:14 EST 2021. Contains 349563 sequences. (Running on oeis4.)