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A281715 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards. 13
1, 1, 2, 1, 3, 4, 2, 7, 4, 8, 3, 14, 8, 6, 16, 5, 29, 38, 14, 9, 32, 8, 61, 90, 97, 17, 14, 64, 13, 126, 305, 294, 245, 22, 22, 128, 21, 265, 902, 1410, 937, 631, 30, 35, 256, 34, 553, 2710, 5781, 6417, 3166, 1625, 43, 56, 512, 55, 1162, 8376, 23798, 37781, 29849, 10738, 4234 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Table starts

...1..1..1.....2......3........5.........8..........13...........21

...2..3..7....14.....29.......61.......126.........265..........553

...4..4..8....38.....90......305.......902........2710.........8376

...8..6.14....97....294.....1410......5781.......23798.......103034

..16..9.17...245....937.....6417.....37781......214045......1321909

..32.14.22...631...3166....29849....252867.....1987696.....17241122

..64.22.30..1625..10738...142023...1721319....18779855....230037168

.128.35.43..4234..37285...677045..11737418...178547832...3076165855

.256.56.64.11017.129586..3244671..80326035..1704685390..41247350230

.512.90.98.28652.452042.15605137.550174620.16297041786.554236736742

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

FORMULA

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) -a(n-3) for n>4

k=3: a(n) = 2*a(n-1) -a(n-3) for n>6

k=4: [order 15] for n>16

k=5: [order 24] for n>28

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) -2*a(n-4) +4*a(n-5)

n=3: [order 20] for n>21

n=4: [order 72] for n>73

EXAMPLE

Some solutions for n=4 k=4

..0..0..1..0. .0..0..1..0. .0..1..0..1. .0..0..1..1. .0..0..0..1

..1..1..0..1. .1..1..0..1. .1..0..1..0. .1..1..0..0. .0..0..1..1

..1..1..1..0. .1..1..1..0. .0..1..0..1. .1..1..0..0. .0..0..1..1

..1..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..1. .1..1..0..0

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A001611(n+1).

Row 1 is A000045(n-1).

Sequence in context: A269752 A122164 A210793 * A076632 A105646 A059126

Adjacent sequences:  A281712 A281713 A281714 * A281716 A281717 A281718

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 28 2017

STATUS

approved

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Last modified January 17 16:21 EST 2021. Contains 340246 sequences. (Running on oeis4.)