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

Author

R. H. Hardin, Oct 16 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

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)