A280124 T(n,k)=Number of nXk 0..2 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, 8, 28, 37, 28, 8, 14, 80, 168, 168, 80, 14, 36, 252, 705, 1030, 705, 252, 36, 74, 776, 2852, 5802, 5802, 2852, 776, 74, 168, 2356, 11249, 31608, 44382, 31608, 11249, 2356, 168, 358, 7200, 44120, 171100, 330254, 330254, 171100, 44120

Offset

1,4

Comments

Table starts

...0.....0......2........2.........8.........14.........36.........74

...0.....4......8.......28........80........252........776.......2356

...2.....8.....37......168.......705.......2852......11249......44120

...2....28....168.....1030......5802......31608.....171100.....916768

...8....80....705.....5802.....44382.....330254....2433834...17647668

..14...252...2852....31608....330254....3348206...33510642..330506508

..36...776..11249...171100...2433834...33510642..454149404.6104734752

..74..2356..44120...916768..17647668..330506508.6104734752

.168..7200.172216..4882310.127427398.3241940520

.358.21836.669642.25849910.911386034

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +7*a(n-2) -24*a(n-4) -32*a(n-5) -16*a(n-6) for n>8

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

k=4: [order 28] for n>34

k=5: [order 86] for n>96

Example

Some solutions for n=4 k=4
..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..1..1..0. .0..0..0..0
..0..2..2..1. .0..1..1..1. .0..1..1..1. .1..1..0..0. .0..0..0..1
..2..2..2..1. .1..1..1..2. .1..1..1..1. .1..1..0..0. .2..2..1..1
..2..2..1..1. .1..1..2..2. .1..1..0..1. .1..1..0..0. .2..1..1..1

Crossrefs

Column 1 is 2*A219754(n+1).

Sequence in context: A331004 A278540 A280161 * A279268 A279856 A054507

Adjacent sequences: A280121 A280122 A280123 * A280125 A280126 A280127

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 26 2016

Status

approved