A263373 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column divisible by 7, read as a base-3 number with top and left being the most significant digits.

1, 1, 1, 2, 2, 2, 5, 7, 7, 5, 10, 29, 82, 29, 10, 19, 112, 865, 865, 112, 19, 37, 367, 9888, 24711, 9888, 367, 37, 73, 1359, 107514, 826249, 826249, 107514, 1359, 73, 146, 5370, 1260442, 27274339, 84790557, 27274339, 1260442, 5370, 146, 293, 21447, 15048493

Offset

1,4

Comments

Table starts

...1.....1..........2.............5.............10..............19

...1.....2..........7............29............112.............367

...2.....7.........82...........865...........9888..........107514

...5....29........865.........24711.........826249........27274339

..10...112.......9888........826249.......84790557......8491666657

..19...367.....107514......27274339.....8491666657...2535097569590

..37..1359....1260442.....943196037...883978450474.787253224440475

..73..5370...15048493...32850517101.92359613590072

.146.21447..180640864.1149496602927

.293.86013.2167406803

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -3*a(n-4) +3*a(n-5) -2*a(n-6)

k=2: a(n) = 4*a(n-1) +101*a(n-6) -404*a(n-7) -2159*a(n-12) +8636*a(n-13) +2059*a(n-18) -8236*a(n-19)

Example

Some solutions for n=4 k=4
..1..2..2..0..1....1..1..0..1..1....2..2..0..0..1....0..2..1..2..1
..2..1..2..1..0....2..2..1..2..0....1..2..2..0..1....2..2..2..1..1
..2..1..0..0..0....2..1..0..2..1....0..0..0..0..0....1..2..0..1..2
..2..1..0..2..1....2..1..0..0..0....0..0..0..2..1....2..1..1..1..2
..2..2..1..2..0....2..0..1..1..1....0..1..2..1..1....1..1..2..2..1

Crossrefs

Sequence in context: A279515 A260338 A023569 * A145876 A240540 A039878

Adjacent sequences: A263370 A263371 A263372 * A263374 A263375 A263376

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 16 2015

Status

approved