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A231023
T(n,k)=Number of (n+3)X(k+3) 0..3 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero
5
6, 16, 16, 76, 242, 76, 314, 724, 724, 314, 1170, 10534, 8374, 10534, 1170, 4584, 28128, 85196, 85196, 28128, 4584, 18208, 419878, 854206, 3160834, 854206, 419878, 18208, 71242, 1144652, 8838040, 22328204, 22328204, 8838040, 1144652, 71242, 278758
OFFSET
1,1
COMMENTS
Table starts
.....6.......16........76..........314...........1170.............4584
....16......242.......724........10534..........28128...........419878
....76......724......8374........85196.........854206..........8838040
...314....10534.....85196......3160834.......22328204........859128648
..1170....28128....854206.....22328204......584293702......15744800360
..4584...419878...8838040....859128648....15744800360....1576885946694
.18208..1144652..91616256...6209914254...421312592376...29418861515276
.71242.16946918.944382122.235891268252.11212196319546.2914693904795344
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 3*a(n-1) +14*a(n-3) +a(n-4) -a(n-5)
k=2: [order 16]
k=3: [order 30]
k=4: [order 70]
EXAMPLE
Some solutions for n=2 k=4
..x..0..x..3..x..3..x....x..0..x..0..x..0..x....x..0..x..2..x..2..x
..1..x..3..x..0..x..0....3..x..1..x..3..x..1....0..x..1..x..3..x..1
..x..2..x..3..x..1..x....x..0..x..2..x..2..x....x..1..x..0..x..2..x
..3..x..1..x..0..x..2....3..x..3..x..1..x..1....2..x..0..x..3..x..1
..x..0..x..3..x..3..x....x..2..x..0..x..0..x....x..3..x..2..x..2..x
CROSSREFS
Column 1 is A230942
Column 3 is A230944
Column 5 is A230946
Column 7 is A230948
Sequence in context: A183127 A222884 A230949 * A217186 A101239 A242331
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 03 2013
STATUS
approved