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

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

R. H. Hardin, Table of n, a(n) for n = 1..143

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

Adjacent sequences: A231020 A231021 A231022 * A231024 A231025 A231026

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 03 2013

Status

approved