A231131 T(n,k)=Number of (n+1)X(k+1) white-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, 8, 6, 16, 40, 40, 16, 44, 176, 308, 176, 44, 120, 808, 2260, 2260, 808, 120, 328, 3584, 16812, 27664, 16812, 3584, 328, 896, 16368, 124644, 336004, 336004, 124644, 16368, 896, 2448, 72640, 924900, 4150352, 6794904, 4150352, 924900, 72640, 2448

Offset

1,2

Comments

Table starts

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

..2...8....40....176.....808......3584......16368.......72640........331648

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

.16.176..2260..27664..336004...4150352...50257244...621150768....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
..0..x..1..x..1....0..x..0..x..1....0..x..1..x..0....0..x..0..x..1
..x..1..x..2..x....x..1..x..0..x....x..1..x..2..x....x..1..x..2..x
..2..x..2..x..1....2..x..1..x..1....0..x..0..x..0....0..x..2..x..1

Crossrefs

Column 1 is A002605

Sequence in context: A306688 A092522 A116542 * A142243 A269722 A091441

Adjacent sequences: A231128 A231129 A231130 * A231132 A231133 A231134

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 04 2013

Status

approved