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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 14 19:09 EDT 2020. Contains 336483 sequences. (Running on oeis4.)