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A238654 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors, and new values 0..1 introduced in row major order 7
1, 2, 2, 3, 8, 3, 5, 18, 18, 5, 8, 50, 51, 50, 8, 13, 128, 189, 189, 128, 13, 21, 338, 630, 1015, 630, 338, 21, 34, 882, 2187, 4742, 4742, 2187, 882, 34, 55, 2312, 7473, 23373, 30116, 23373, 7473, 2312, 55, 89, 6050, 25692, 112827, 204216, 204216, 112827 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

..2.....8.....18.......50.......128.........338..........882...........2312

..3....18.....51......189.......630........2187.........7473..........25692

..5....50....189.....1015......4742.......23373.......112827.........549068

..8...128....630.....4742.....30116......204216......1349732........9010526

.13...338...2187....23373....204216.....1929041.....17672899......163862944

.21...882...7473...112827...1349732....17672899....223336353.....2861990416

.34..2312..25692...549068...9010526...163862944...2861990416....50789138692

.55..6050..88119..2663629..59917746..1512215465..36475373351...895686099682

.89.15842.302511.12937577.399048464.13981375097.465876675157.15835026599714

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..287

FORMULA

Empirical for column k:

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

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

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

k=4: [order 20]

k=5: [order 68]

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1)

Column 2 is A175395(n+1)

Sequence in context: A141617 A267644 A204197 * A220553 A176383 A100551

Adjacent sequences:  A238651 A238652 A238653 * A238655 A238656 A238657

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 02 2014

STATUS

approved

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Last modified September 23 02:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)