A204381 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 or nw-to-se diagonally exactly three ways, and new values 0..1 introduced in row major order

33, 51, 51, 78, 48, 78, 113, 54, 54, 113, 182, 63, 61, 63, 182, 286, 88, 75, 75, 88, 286, 439, 128, 98, 87, 98, 128, 439, 710, 193, 139, 111, 111, 139, 193, 710, 1128, 300, 205, 153, 136, 153, 205, 300, 1128, 1775, 470, 310, 217, 176, 176, 217, 310, 470, 1775, 2873

Offset

1,1

Comments

Table starts

..33..51..78.113.182.286.439.710.1128.1775.2873.4628.7422.12063.19589.31772

..51..48..54..63..88.128.193.300..470..747.1196.1920.3093..4992..8062.13031

..78..54..61..75..98.139.205.310..481..759.1206.1931.3105..5002..8073.13043

.113..63..75..87.111.153.217.323..495..771.1219.1945.3117..5015..8087.13055

.182..88..98.111.136.176.241.348..518..795.1244.1968.3141..5040..8110.13079

.286.128.139.153.176.217.283.388..559..837.1284.2009.3183..5080..8151.13121

.439.193.205.217.241.283.347.453..625..901.1349.2075.3247..5145..8217.13185

.710.300.310.323.348.388.453.560..730.1007.1456.2180.3353..5252..8322.13291

Links

R. H. Hardin, Table of n, a(n) for n = 1..1103

Formula

Empirical for column k:

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

k=2..7: a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) for n>8

Example

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

Crossrefs

Sequence in context: A226698 A096278 A349551 * A034815 A014976 A364286

Adjacent sequences: A204378 A204379 A204380 * A204382 A204383 A204384

Keyword

nonn,tabl

Author

R. H. Hardin Jan 14 2012

Status

approved