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

1,2

Comments

Column 3 of A262917.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Robert Israel, Maple-assisted proof of empirical formula for A262912

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

Example

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

Crossrefs

Cf. A262917.

Sequence in context: A271332 A244024 A122365 * A119132 A073065 A190801

Adjacent sequences: A262909 A262910 A262911 * A262913 A262914 A262915

Keyword

nonn

Author

R. H. Hardin, Oct 04 2015

Status

approved