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

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

R. H. Hardin, Table of n, a(n) for n = 1..1624

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

Adjacent sequences: A253022 A253023 A253024 * A253026 A253027 A253028

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 26 2014

Status

approved