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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000244

Row 1 is A202882 for n>1

Sequence in context: A146068 A146911 A146250 * A146695 A146442 A147128

Adjacent sequences: A232020 A232021 A232022 * A232024 A232025 A232026

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 17 2013

Status

approved