A204370 T(n,k)=Number of (n+2)X(k+2) 0..2 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..2 introduced in row major order

74, 212, 212, 555, 466, 555, 891, 673, 673, 891, 2419, 713, 342, 713, 2419, 6121, 1715, 622, 622, 1715, 6121, 13693, 4355, 1042, 704, 1042, 4355, 13693, 38041, 11671, 2574, 1264, 1264, 2574, 11671, 38041, 99753, 31891, 6786, 2956, 1984, 2956, 6786, 31891

Offset

1,1

Comments

Table starts

....74...212...555...891..2419..6121.13693.38041.99753.256077.702265.1904821

...212...466...673...713..1715..4355.11671.31891.86275.235547.643475.1756499

...555...673...342...622..1042..2574..6786.17586.47674.130066.353650..965730

...891...713...622...704..1264..2956..6772.17852.48260.129860.354004..966724

..2419..1715..1042..1264..1984..3280..7376.18776.48392.130552.355336..966472

..6121..4355..2574..2956..3280..4856..9272.19880.50056.132856.356056..968312

.13693.11671..6786..6772..7376..9272.12896.24064.54880.136096.360416..973952

.38041.31891.17586.17852.18776.19880.24064.35872.65104.147440.373040..983408

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-1) -7*a(n-2) +3*a(n-3) -6*a(n-4) +12*a(n-5) +14*a(n-6) -84*a(n-7) +164*a(n-8) -292*a(n-9) +392*a(n-10) -392*a(n-11) +640*a(n-12) -896*a(n-13) +64*a(n-14) +2176*a(n-15) -3584*a(n-16) +2304*a(n-17) -512*a(n-18)

k=2..7: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>9

Example

Some solutions for n=5 k=3
..0..0..0..1..0....0..0..0..0..0....0..1..0..0..1....0..0..0..0..0
..1..1..1..1..1....1..1..1..1..1....0..1..0..0..1....1..1..1..1..0
..1..1..1..1..1....2..2..2..2..2....0..1..0..0..1....0..0..0..0..0
..0..0..0..0..0....1..1..1..1..1....0..1..0..0..1....0..0..0..0..0
..1..1..1..1..1....2..2..2..2..2....0..1..0..0..1....1..1..1..1..1
..1..1..1..1..1....2..2..2..2..2....0..0..0..0..1....1..1..1..1..1
..0..1..0..0..0....1..2..0..0..0....1..1..0..0..1....2..1..2..2..2

Crossrefs

Sequence in context: A260171 A044406 A044787 * A204363 A051970 A300604

Adjacent sequences: A204367 A204368 A204369 * A204371 A204372 A204373

Keyword

nonn,tabl

Author

R. H. Hardin Jan 14 2012

Status

approved