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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
25, 37, 37, 51, 50, 51, 63, 83, 83, 63, 105, 91, 133, 91, 105, 153, 133, 120, 120, 133, 153, 189, 223, 219, 155, 219, 223, 189, 315, 243, 350, 230, 230, 350, 243, 315, 459, 357, 302, 296, 327, 296, 302, 357, 459, 567, 595, 531, 369, 537, 537, 369, 531, 595, 567, 945, 653
OFFSET
1,1
COMMENTS
Table starts
..25..37..51..63..105..153..189..315..459..567..945.1377.1701..2835..4131..5103
..37..50..83..91..133..223..243..357..595..653..959.1589.1761..2583..4253..4765
..51..83.133.120..219..350..302..531..846..754.1323.2100.1888..3287..5198..4734
..63..91.120.155..230..296..369..546..712..893.1322.1722.2155..3190..4158..5203
.105.133.219.230..327..537..554..753.1193.1250.1721.2747.2894..3987..6343..6694
.153.223.350.296..537..864..720.1256.1912.1592.2688.4096.3520..5968..9136..7904
.189.243.302.369..554..720..920.1312.1616.1976.2784.3472.4272..6096..7664..9464
.315.357.531.546..753.1256.1312.1832.2936.2976.3896.5984.6128..8128.12616.13056
.459.595.846.712.1193.1912.1616.2936.4672.3840.6544.9696.7904.13008.19264.16192
.567.653.754.893.1250.1592.1976.2976.3840.4880.6816.8192.9904.13536.16384.19888
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 3*a(n-3) for n>5
k=2: a(n) = 6*a(n-3) -10*a(n-6) +3*a(n-9) for n>11
k=3: a(n) = 5*a(n-3) -6*a(n-6) -a(n-9) +a(n-12) for n>15
k=4: a(n) = 3*a(n-3) -a(n-6) -a(n-9) for n>12
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
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
k=7: a(n) = 3*a(n-3) -a(n-6) -a(n-9) -a(n-12) -a(n-15) for n>20
EXAMPLE
Some solutions for n=4 k=4
..0..1..2..0..1..3....0..1..2..0..3..2....0..0..0..0..0..0....0..0..0..0..0..0
..0..0..0..0..0..0....2..2..2..2..2..2....1..2..0..1..3..0....1..0..2..1..0..2
..0..2..1..0..2..1....1..0..2..1..0..2....2..1..0..3..1..0....3..0..1..2..0..1
..0..1..2..0..1..2....0..1..2..0..1..2....0..0..0..0..0..0....0..0..0..0..0..0
..0..0..0..0..0..0....2..2..2..2..2..2....1..3..0..1..2..0....1..0..3..1..0..2
..0..2..1..0..2..3....3..0..2..1..0..2....3..1..0..2..1..0....3..0..1..3..0..1
CROSSREFS
Sequence in context: A179803 A061863 A079270 * A127022 A253018 A120148
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 26 2014
STATUS
approved