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A279709
T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
13
1, 1, 2, 1, 2, 4, 2, 3, 5, 8, 3, 4, 11, 13, 16, 5, 6, 22, 42, 34, 32, 8, 9, 47, 125, 161, 89, 64, 13, 14, 102, 385, 717, 617, 233, 128, 21, 22, 224, 1195, 3245, 4121, 2364, 610, 256, 34, 35, 494, 3751, 14988, 27346, 23690, 9057, 1597, 512, 55, 56, 1089, 11823, 70220
OFFSET
1,3
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 5*a(n-1) -5*a(n-2) +2*a(n-3)
k=4: [order 8] for n>9
k=5: [order 12] for n>13
k=6: [order 32] for n>33
k=7: [order 60] for n>62
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) for n>3
n=2: a(n) = 2*a(n-1) -a(n-3)
n=3: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +4*a(n-4) -a(n-5) -a(n-7) -a(n-8)
n=4: [order 23] for n>25
n=5: [order 56] for n>64
EXAMPLE
Table starts
...1....1......1.......2.........3..........5............8............13
...2....2......3.......4.........6..........9...........14............22
...4....5.....11......22........47........102..........224...........494
...8...13.....42.....125.......385.......1195.........3751.........11823
..16...34....161.....717......3245......14988........70220........329692
..32...89....617....4121.....27346.....187484......1302321.......9047660
..64..233...2364...23690....230128....2342179.....24137862.....248664928
.128..610...9057..136181...1936687...29270275....447547408....6837220721
.256.1597..34699..782826..16300179..365809911...8297886949..187983779265
.512.4181.132938.4500021.137192011.4571688626.153848240903.5168463666199
Some solutions for n=4 k=4
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..0..1..0. .0..1..1..0. .0..1..0..0. .0..1..0..1. .0..1..1..0
..1..0..1..1. .0..0..1..1. .0..0..1..1. .0..1..0..1. .0..0..0..1
..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .1..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A001519.
Row 1 is A000045(n-1).
Row 2 is A001611.
Sequence in context: A276053 A117268 A361076 * A261880 A119538 A068309
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 17 2016
STATUS
approved