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A204284 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, diagonally or antidiagonally exactly three ways, and new values 0..2 introduced in row major order 9

%I

%S 108,274,274,783,622,783,1758,865,865,1758,5263,193,128,193,5263,

%T 14141,539,256,256,539,14141,29731,735,334,244,334,735,29731,93809,

%U 1883,778,442,442,778,1883,93809,248919,5187,1990,982,736,982,1990,5187,248919

%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, diagonally or antidiagonally exactly three ways, and new values 0..2 introduced in row major order

%C Table starts

%C ...108..274..783.1758.5263.14141.29731.93809.248919.573623.1749927.4584571

%C ...274..622..865..193..539...735..1883..5187..12715..34507...94379..254955

%C ...783..865..128..256..334...778..1990..4758..12782..34702...93502..255070

%C ..1758..193..256..244..442...982..1914..4922..13138..34498...93778..255730

%C ..5263..539..334..442..736...996..2168..5368..13024..34864...94528..255360

%C .14141..735..778..982..996..1496..2860..5500..13636..35860...94404..256196

%C .29731.1883.1990.1914.2168..2860..3664..6784..15304..36408...95912..258472

%C .93809.5187.4758.4922.5368..5500..6784.10288..17688..39752..100024..260344

%H R. H. Hardin, <a href="/A204284/b204284.txt">Table of n, a(n) for n = 1..337</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) -3*a(n-2) +10*a(n-3) -44*a(n-4) +60*a(n-5) -30*a(n-6) -172*a(n-7) -152*a(n-8) +1224*a(n-9) -448*a(n-10) -656*a(n-11) +880*a(n-12) -2592*a(n-13) +2688*a(n-14) -768*a(n-15) for n>16

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

%F k=3..7: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>8

%e Some solutions for n=4 k=3

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 13 2012

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Last modified February 1 12:28 EST 2023. Contains 359993 sequences. (Running on oeis4.)