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A253025 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every consecutive three elements in every row and column not having exactly two distinct values, and in every diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order 9

%I

%S 25,37,37,51,50,51,63,83,83,63,105,91,133,91,105,153,133,120,120,133,

%T 153,189,223,219,155,219,223,189,315,243,350,230,230,350,243,315,459,

%U 357,302,296,327,296,302,357,459,567,595,531,369,537,537,369,531,595,567,945,653

%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every consecutive three elements in every row and column not having exactly two distinct values, and in every diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order

%C Table starts

%C ..25..37..51..63..105..153..189..315..459..567..945.1377.1701..2835..4131..5103

%C ..37..50..83..91..133..223..243..357..595..653..959.1589.1761..2583..4253..4765

%C ..51..83.133.120..219..350..302..531..846..754.1323.2100.1888..3287..5198..4734

%C ..63..91.120.155..230..296..369..546..712..893.1322.1722.2155..3190..4158..5203

%C .105.133.219.230..327..537..554..753.1193.1250.1721.2747.2894..3987..6343..6694

%C .153.223.350.296..537..864..720.1256.1912.1592.2688.4096.3520..5968..9136..7904

%C .189.243.302.369..554..720..920.1312.1616.1976.2784.3472.4272..6096..7664..9464

%C .315.357.531.546..753.1256.1312.1832.2936.2976.3896.5984.6128..8128.12616.13056

%C .459.595.846.712.1193.1912.1616.2936.4672.3840.6544.9696.7904.13008.19264.16192

%C .567.653.754.893.1250.1592.1976.2976.3840.4880.6816.8192.9904.13536.16384.19888

%H R. H. Hardin, <a href="/A253025/b253025.txt">Table of n, a(n) for n = 1..1624</a>

%F Empirical for column k:

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

%F k=2: a(n) = 6*a(n-3) -10*a(n-6) +3*a(n-9) for n>11

%F k=3: a(n) = 5*a(n-3) -6*a(n-6) -a(n-9) +a(n-12) for n>15

%F k=4: a(n) = 3*a(n-3) -a(n-6) -a(n-9) for n>12

%F k=5: a(n) = 5*a(n-3) -6*a(n-6) -2*a(n-9) +2*a(n-12) +3*a(n-15) +a(n-18) for n>22

%F k=6: a(n) = 5*a(n-3) -7*a(n-6) +2*a(n-9) -2*a(n-12) +3*a(n-15) +a(n-18) +a(n-21) for n>27

%F k=7: a(n) = 3*a(n-3) -a(n-6) -a(n-9) -a(n-12) -a(n-15) for n>20

%e Some solutions for n=4 k=4

%e ..0..1..2..0..1..3....0..1..2..0..3..2....0..0..0..0..0..0....0..0..0..0..0..0

%e ..0..0..0..0..0..0....2..2..2..2..2..2....1..2..0..1..3..0....1..0..2..1..0..2

%e ..0..2..1..0..2..1....1..0..2..1..0..2....2..1..0..3..1..0....3..0..1..2..0..1

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

%e ..0..0..0..0..0..0....2..2..2..2..2..2....1..3..0..1..2..0....1..0..3..1..0..2

%e ..0..2..1..0..2..3....3..0..2..1..0..2....3..1..0..2..1..0....3..0..1..3..0..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 26 2014

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Last modified October 15 18:04 EDT 2021. Contains 348033 sequences. (Running on oeis4.)