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A240519 T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..1 introduced in row major order 8
1, 2, 2, 3, 3, 3, 5, 6, 6, 5, 8, 10, 10, 10, 8, 13, 21, 28, 28, 21, 13, 21, 42, 73, 99, 73, 42, 21, 34, 86, 196, 326, 326, 196, 86, 34, 55, 179, 515, 1080, 1376, 1080, 515, 179, 55, 89, 370, 1376, 3765, 6205, 6205, 3765, 1376, 370, 89, 144, 770, 3686, 13282, 28942, 37624 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1...2....3......5.......8.......13.........21..........34...........55

..2...3....6.....10......21.......42.........86.........179..........370

..3...6...10.....28......73......196........515........1376.........3686

..5..10...28.....99.....326.....1080.......3765.......13282........46928

..8..21...73....326....1376.....6205......28942......135093.......636475

.13..42..196...1080....6205....37624.....231665.....1440880......9082172

.21..86..515...3765...28942...231665....1906245....16000486....135790448

.34.179.1376..13282..135093..1440880...16000486...180760099...2056580724

.55.370.3686..46928..636475..9082172..135790448..2056580724..31517059634

.89.770.9914.166611.3024792.57688194.1158315893.23588995330.488025204070

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

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

k=3: [order 20]

k=4: [order 48]

EXAMPLE

Some solutions for n=4 k=4

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1)

Sequence in context: A260684 A029093 A301541 * A318037 A326165 A078462

Adjacent sequences:  A240516 A240517 A240518 * A240520 A240521 A240522

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 06 2014

STATUS

approved

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Last modified May 31 04:43 EDT 2020. Contains 334747 sequences. (Running on oeis4.)