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A280554 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards. 7
0, 0, 0, 0, 0, 0, 1, 9, 9, 1, 2, 34, 50, 34, 2, 6, 87, 144, 144, 87, 6, 13, 194, 325, 382, 325, 194, 13, 29, 400, 670, 832, 832, 670, 400, 29, 60, 790, 1316, 1666, 1764, 1666, 1316, 790, 60, 122, 1511, 2502, 3182, 3438, 3438, 3182, 2502, 1511, 122, 241, 2830, 4654 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Table starts

...0....0....0.....1.....2.....6....13.....29.....60....122....241....468

...0....0....9....34....87...194...400....790...1511...2830...5213...9484

...0....9...50...144...325...670..1316...2502...4654...8521..15412..27612

...1...34..144...382...832..1666..3182...5886..10680..19122..33920..59754

...2...87..325...832..1764..3438..6386..11506..20389..35757..62317.108150

...6..194..670..1666..3438..6502.11697..20440..35226..60300.102974.175746

..13..400.1316..3182..6386.11697.20334..34360..57389..95548.159360.266756

..29..790.2502..5886.11506.20440.34360..56102..90614.146264.237392.388378

..60.1511.4654.10680.20389.35226.57389..90614.141398.220709.347310.553046

.122.2830.8521.19122.35757.60300.95548.146264.220709.332810.506359.781682

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..391

FORMULA

Empirical for column k:

k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)

k=2: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +10*a(n-4) -2*a(n-5) -5*a(n-6) +a(n-7) +a(n-8) for n>9

k=3: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +10*a(n-4) -2*a(n-5) -5*a(n-6) +a(n-7) +a(n-8) for n>10

k=4: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>11

k=5: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12

k=6: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12

k=7: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12

EXAMPLE

Some solutions for n=4 k=4

..0..1..0..1. .0..1..0..0. .0..1..1..0. .0..1..0..1. .0..1..0..1

..1..0..1..0. .0..1..0..1. .1..1..0..1. .0..1..0..1. .1..0..1..1

..0..1..1..0. .1..0..1..0. .0..0..1..0. .1..0..1..0. .0..1..0..0

..1..0..1..0. .0..0..1..0. .1..1..0..1. .1..1..0..0. .0..1..0..1

CROSSREFS

Column 1 is A055243(n-4).

Column 2 is A279128.

Sequence in context: A197364 A174266 A334425 * A195722 A133627 A268918

Adjacent sequences:  A280551 A280552 A280553 * A280555 A280556 A280557

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 05 2017

STATUS

approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)