A232023 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

3, 3, 9, 9, 22, 27, 22, 66, 121, 81, 51, 212, 852, 704, 243, 121, 716, 6443, 11517, 4059, 729, 292, 2447, 52680, 196196, 156913, 23422, 2187, 704, 8312, 429976, 3668759, 6129361, 2125749, 135166, 6561, 1691, 28118, 3466702, 66962048, 266779524

Offset: 1

Author

R. H. Hardin, Nov 17 2013

Keywords

• nonn
• tabl

Comments

Table starts

.....3.......3..........9............22...............51.................121

.....9......22.........66...........212..............716................2447

....27.....121........852..........6443............52680..............429976

....81.....704......11517........196196..........3668759............66962048

...243....4059.....156913.......6129361........266779524.........11145921002

...729...23422....2125749.....189686855......19227454407.......1843879894941

..2187..135166...28852936....5882557816....1386576216443.....304550219824247

..6561..779977..391447970..182394008292..100026008988909...50342644960736903

.19683.4500958.5311170384.5654881014985.7214505515214571.8320423932674561675

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..262

Crossrefs

Column 1 is A000244

Row 1 is A202882 for n>1

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1)

k=2: a(n) = 3*a(n-1) +13*a(n-2) +16*a(n-3) +7*a(n-4) +a(n-5)

k=3: [order 7] for n>8

k=4: [order 18] for n>19

k=5: [order 41] for n>42

k=6: [order 79] for n>81

Empirical for row n:

n=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6

n=2: [order 17] for n>18

n=3: [order 61] for n>64