A230949 T(n,k)=Number of (n+3)X(k+3) 0..3 white 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, 34, 76, 314, 724, 724, 314, 1170, 1994, 8374, 1994, 1170, 4584, 28128, 85196, 85196, 28128, 4584, 18208, 76682, 854206, 606224, 854206, 76682, 18208, 71242, 1144652, 8838040, 22328204, 22328204, 8838040, 1144652, 71242, 278758

Offset

1,1

Comments

Table starts

.....6......16........76.........314...........1170............4584

....16......34.......724........1994..........28128...........76682

....76.....724......8374.......85196.........854206.........8838040

...314....1994.....85196......606224.......22328204.......161835904

..1170...28128....854206....22328204......584293702.....15744800360

..4584...76682...8838040...161835904....15744800360....295706164414

.18208.1144652..91616256..6209914254...421312592376..29418861515276

.71242.3107746.944382122.44707108238.11212196319546.546918612768188

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

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
..0..x..3..x..3..x..3....0..x..2..x..1..x..1....0..x..0..x..3..x..1
..x..1..x..0..x..0..x....x..1..x..3..x..2..x....x..1..x..0..x..2..x
..2..x..2..x..1..x..3....2..x..0..x..1..x..3....2..x..2..x..1..x..1
..x..3..x..1..x..2..x....x..3..x..1..x..0..x....x..3..x..1..x..0..x
..2..x..0..x..0..x..1....2..x..2..x..0..x..3....2..x..0..x..3..x..3

Crossrefs

Sequence in context: A301831 A183127 A222884 * A231023 A217186 A101239

Adjacent sequences: A230946 A230947 A230948 * A230950 A230951 A230952

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 01 2013

Status

approved