A230935 - OEIS

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

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

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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