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A231070 T(n,k)=Number of black square subarrays of (n+1)X(k+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero 5
1, 1, 1, 2, 3, 2, 3, 4, 4, 3, 5, 11, 11, 11, 5, 8, 15, 24, 24, 15, 8, 13, 42, 59, 89, 59, 42, 13, 21, 57, 139, 191, 191, 139, 57, 21, 34, 161, 332, 748, 685, 748, 332, 161, 34, 55, 218, 796, 1573, 2379, 2379, 1573, 796, 218, 55, 89, 617, 1903, 6259, 8357, 13785, 8357 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

..1...1...2....3.....5......8......13.......21.......34........55.........89

..1...3...4...11....15.....42......57......161......218.......617........835

..2...4..11...24....59....139.....332......796.....1903......4563......10934

..3..11..24...89...191....748....1573.....6259....13176.....52497.....110739

..5..15..59..191...685...2379....8357....29493...103842....366761....1295168

..8..42.139..748..2379..13785...43004...253150...793041...4669709...14671984

.13..57.332.1573..8357..43004..223270..1168723..6098749..31928221..167211867

.21.161.796.6259.29493.253150.1168723.10204445.47403200.414060681.1930022303

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..684

FORMULA

Empirical for column k:

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

k=2: a(n) = 5*a(n-2) -5*a(n-4) +2*a(n-6)

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

k=4: [order 18, even terms]

k=5: [order 32]

k=6: [order 70, even terms]

EXAMPLE

Some solutions for n=4 k=4

..x..0..x..1..x....x..0..x..0..x....x..0..x..1..x....x..0..x..0..x

..1..x..0..x..0....1..x..1..x..1....1..x..0..x..1....0..x..1..x..0

..x..1..x..0..x....x..0..x..0..x....x..1..x..0..x....x..1..x..1..x

..0..x..1..x..1....1..x..1..x..1....0..x..0..x..1....1..x..0..x..1

..x..1..x..0..x....x..0..x..0..x....x..1..x..1..x....x..0..x..0..x

CROSSREFS

Column 1 is A000045

Column 3 is A230984

Column 5 is A230986

Column 7 is A230988

Sequence in context: A054237 A129600 A081388 * A230252 A295424 A002372

Adjacent sequences:  A231067 A231068 A231069 * A231071 A231072 A231073

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 03 2013

STATUS

approved

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Last modified August 2 02:53 EDT 2021. Contains 346409 sequences. (Running on oeis4.)