A280161 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 4, 2, 2, 8, 8, 2, 5, 18, 31, 18, 5, 8, 40, 94, 94, 40, 8, 15, 92, 305, 424, 305, 92, 15, 26, 208, 950, 1854, 1854, 950, 208, 26, 46, 470, 2901, 7628, 10677, 7628, 2901, 470, 46, 80, 1060, 8728, 30874, 58852, 58852, 30874, 8728, 1060, 80, 139, 2384, 26068

Offset

1,4

Comments

Table starts

..0....0.....2......2.......5.........8.........15..........26...........46

..0....4.....8.....18......40........92........208.........470.........1060

..2....8....31.....94.....305.......950.......2901........8728........26068

..2...18....94....424....1854......7628......30874......123312.......488256

..5...40...305...1854...10677.....58852.....318220.....1695030......8941285

..8...92...950...7628...58852....434790....3138340....22348406....157294986

.15..208..2901..30874..318220...3138340...30089398...285461736...2671391625

.26..470..8728.123312.1695030..22348406..285461736..3612425586..45045404794

.46.1060.26068.488256.8941285.157294986.2671391625.45045404794.748382706193

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) +a(n-2) -2*a(n-3) -a(n-4) for n>5

k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6) for n>8

k=3: [order 14] for n>19

k=4: [order 30] for n>36

k=5: [order 70] for n>80

Example

Some solutions for n=4 k=4
..0..0..1..1. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..0..0
..0..1..0..1. .0..0..0..1. .0..1..1..0. .0..0..1..1. .1..1..0..1
..1..1..1..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .1..0..1..1
..1..1..0..0. .1..1..1..1. .0..1..0..0. .0..1..0..0. .0..0..1..1

Crossrefs

Column 1 is A006367(n-1).

Sequence in context: A279902 A331004 A278540 * A280124 A279268 A279856

Adjacent sequences: A280158 A280159 A280160 * A280162 A280163 A280164

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 27 2016

Status

approved