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A230935 T(n,k)=Number of black-square subarrays of (n+2)X(k+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero 9
2, 2, 2, 8, 6, 8, 8, 16, 16, 8, 42, 48, 102, 48, 42, 42, 146, 232, 232, 146, 42, 208, 438, 1682, 1242, 1682, 438, 208, 208, 1312, 3768, 6896, 6896, 3768, 1312, 208, 1042, 3936, 27106, 37984, 98296, 37984, 27106, 3936, 1042, 1042, 11810, 60824, 208172, 396950 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...2....2.....8.......8.......42........42........208..........208

...2....6....16......48......146.......438.......1312.........3936

...8...16...102.....232.....1682......3768......27106........60824

...8...48...232....1242.....6896.....37984.....208172......1142054

..42..146..1682....6896....98296....396950....5528862.....22368688

..42..438..3768...37984...396950...4092246...41991510....431437274

.208.1312.27106..208172..5528862..41991510.1088383766...8279222070

.208.3936.60824.1142054.22368688.431437274.8279222070.159130979900

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..263

FORMULA

Empirical for column k:

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

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

k=3: a(n) = 16*a(n-2) +3*a(n-4) -10*a(n-6) +24*a(n-8) -16*a(n-10)

k=4: [order 17]

k=5: [order 44]

k=6: [order 71]

EXAMPLE

Some solutions for n=4 k=4

..x..0..x..0..x..2....x..0..x..2..x..2....x..0..x..2..x..2....x..0..x..0..x..2

..3..x..1..x..3..x....1..x..1..x..3..x....1..x..3..x..3..x....3..x..1..x..3..x

..x..0..x..2..x..2....x..2..x..2..x..0....x..2..x..0..x..2....x..2..x..2..x..0

..3..x..1..x..3..x....3..x..1..x..1..x....1..x..3..x..1..x....1..x..3..x..1..x

..x..0..x..2..x..0....x..0..x..2..x..0....x..2..x..0..x..2....x..2..x..0..x..0

..3..x..3..x..1..x....3..x..1..x..3..x....1..x..1..x..3..x....1..x..3..x..3..x

CROSSREFS

Sequence in context: A085484 A326480 A116585 * A008293 A185811 A011140

Adjacent sequences:  A230932 A230933 A230934 * A230936 A230937 A230938

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 01 2013

STATUS

approved

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Last modified September 27 22:36 EDT 2020. Contains 337388 sequences. (Running on oeis4.)