A262912 Number of (n+1)X(3+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

1, 6, 15, 53, 318, 1207, 5797, 34782, 189135, 1089701, 6538206, 38547751, 229660021, 1377960126, 8242589055, 49395098933, 296370593598, 1777250964247, 10661181588037, 63967089528222, 383764138693935, 2302493636842181

Offset: 1

Author

R. H. Hardin, Oct 04 2015

Keywords

• nonn

Comments

Column 3 of A262917.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Robert Israel, Maple-assisted proof of empirical formula for A262912

Crossrefs

Cf. A262917.

Formula

Empirical: a(n) = 8*a(n-1) -16*a(n-2) +104*a(n-3) -640*a(n-4) +1280*a(n-5) -3830*a(n-6) +15280*a(n-7) -30560*a(n-8) +58240*a(n-9) -99200*a(n-10) +198400*a(n-11) -283209*a(n-12) -115128*a(n-13) +230256*a(n-14) -345384*a(n-15).

Empirical formula verified: see link. - Robert Israel, Aug 12 2019