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 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 9

%I

%S 74,212,212,555,466,555,891,673,673,891,2419,713,342,713,2419,6121,

%T 1715,622,622,1715,6121,13693,4355,1042,704,1042,4355,13693,38041,

%U 11671,2574,1264,1264,2574,11671,38041,99753,31891,6786,2956,1984,2956,6786,31891

%N 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

%C Table starts

%C ....74...212...555...891..2419..6121.13693.38041.99753.256077.702265.1904821

%C ...212...466...673...713..1715..4355.11671.31891.86275.235547.643475.1756499

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

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

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

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

%C .13693.11671..6786..6772..7376..9272.12896.24064.54880.136096.360416..973952

%C .38041.31891.17586.17852.18776.19880.24064.35872.65104.147440.373040..983408

%H R. H. Hardin, <a href="/A204370/b204370.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

%F 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)

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

%e Some solutions for n=5 k=3

%e ..0..0..0..1..0....0..0..0..0..0....0..1..0..0..1....0..0..0..0..0

%e ..1..1..1..1..1....1..1..1..1..1....0..1..0..0..1....1..1..1..1..0

%e ..1..1..1..1..1....2..2..2..2..2....0..1..0..0..1....0..0..0..0..0

%e ..0..0..0..0..0....1..1..1..1..1....0..1..0..0..1....0..0..0..0..0

%e ..1..1..1..1..1....2..2..2..2..2....0..1..0..0..1....1..1..1..1..1

%e ..1..1..1..1..1....2..2..2..2..2....0..0..0..0..1....1..1..1..1..1

%e ..0..1..0..0..0....1..2..0..0..0....1..1..0..0..1....2..1..2..2..2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 14 2012

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Last modified March 23 16:58 EDT 2023. Contains 361449 sequences. (Running on oeis4.)