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.

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

R. H. Hardin, Table of n, a(n) for n = 1..221

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

Adjacent sequences: A279706 A279707 A279708 * A279710 A279711 A279712

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 17 2016

Status

approved