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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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 28 2017
STATUS
approved

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Last modified February 24 22:04 EST 2024. Contains 370307 sequences. (Running on oeis4.)