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

Author

R. H. Hardin, Nov 04 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A002605

Column 3 is A231126

Column 5 is A231128

Column 7 is A231130

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]