A204754 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..1 introduced in row major order.

40, 61, 61, 102, 46, 102, 188, 31, 31, 188, 342, 28, 22, 28, 342, 590, 38, 27, 27, 38, 590, 1051, 49, 35, 32, 35, 49, 1051, 1915, 70, 48, 40, 40, 48, 70, 1915, 3308, 106, 69, 53, 48, 53, 69, 106, 3308, 5967, 159, 103, 74, 61, 61, 74, 103, 159, 5967, 10934, 248, 158, 108

Offset

1,1

Comments

Table starts

...40..61.102.188.342.590.1051.1915.3308.5967.10934.19151.34428.62824.110673

...61..46..31..28..38..49...70..106..159..248...394...625..1002..1614...2599

..102..31..22..27..35..48...69..103..158..247...391...624..1001..1611...2598

..188..28..27..32..40..53...74..108..163..252...396...629..1006..1616...2603

..342..38..35..40..48..61...82..116..171..260...404...637..1014..1624...2611

..590..49..48..53..61..74...95..129..184..273...417...650..1027..1637...2624

.1051..70..69..74..82..95..116..150..205..294...438...671..1048..1658...2645

.1915.106.103.108.116.129..150..184..239..328...472...705..1082..1692...2679

Links

R. H. Hardin, Table of n, a(n) for n = 1..1151

Formula

Empirical for columns:

k>2: a(n) = 2*a(n-1) -a(n-3) for n>5

k=2: a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) for n>8

k=1: a(n) = 3*a(n-1) -2*a(n-2) +3*a(n-3) -10*a(n-4) +7*a(n-5) +7*a(n-6) -17*a(n-7) +6*a(n-8) +6*a(n-9) +4*a(n-10) -2*a(n-11) +4*a(n-12) -16*a(n-13) +8*a(n-14) for n>15

Example

Some solutions for n=3 k=3
..0..0..0..1..1....0..1..0..1..1....0..1..0..0..1....0..0..0..0..0
..0..0..1..1..1....0..1..0..1..1....0..1..0..0..1....1..1..1..1..1
..0..1..1..1..0....0..1..0..1..1....0..1..0..0..1....1..1..1..1..1
..1..1..1..0..0....0..1..0..1..1....0..1..0..0..1....0..0..0..0..0
..1..1..0..0..0....0..1..0..1..1....0..1..0..0..1....1..1..1..1..1

Crossrefs

Sequence in context: A182205 A195571 A060672 * A204747 A205066 A232870

Adjacent sequences: A204751 A204752 A204753 * A204755 A204756 A204757

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 18 2012

Status

approved