A231137 T(n,k)=Number of (n+1)X(k+1) black-square subarrays of 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order

1, 2, 2, 6, 9, 6, 16, 40, 40, 16, 44, 182, 308, 182, 44, 120, 808, 2260, 2260, 808, 120, 328, 3688, 16812, 27171, 16812, 3688, 328, 896, 16368, 124644, 336004, 336004, 124644, 16368, 896, 2448, 74728, 924900, 4066129, 6794904, 4066129, 924900, 74728, 2448

Offset

1,2

Comments

Table starts

..1...2.....6.....16......44.......120........328.........896..........2448

..2...9....40....182.....808......3688......16368.......74728........331648

..6..40...308...2260...16812....124644.....924900.....6862052......50913012

.16.182..2260..27171..336004...4066129...50257244...608468617....7520563372

.44.808.16812.336004.6794904.137063228.2766762720.55844298404.1127200291672

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

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

k=2: a(n) = 22*a(n-2) -36*a(n-4) +16*a(n-6)

k=3: [order 8]

k=4: [order 18, even terms]

k=5: [order 34]

k=6: [order 90, even terms]

Example

Some solutions for n=2 k=4
..x..0..x..1..x....x..0..x..1..x....x..0..x..0..x....x..0..x..1..x
..2..x..0..x..1....1..x..0..x..2....1..x..2..x..0....2..x..0..x..2
..x..0..x..2..x....x..0..x..1..x....x..1..x..2..x....x..1..x..1..x

Crossrefs

Column 1 is A002605

Column 3 is A231126

Column 5 is A231128

Column 7 is A231130

Sequence in context: A331988 A242978 A345308 * A371400 A188808 A021819

Adjacent sequences: A231134 A231135 A231136 * A231138 A231139 A231140

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 04 2013

Status

approved