A262844 Number of (n+2) X (2+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

6, 34, 132, 396, 1264, 3962, 11886, 35914, 108556, 325668, 976552, 2931922, 8795766, 26370674, 79104084, 237312252, 711756448, 2135076202, 6405228606, 19214238554, 57640739420, 172922218260, 518757049560, 1556255741762, 4668767225286

Offset: 1

Author

R. H. Hardin, Oct 03 2015

Keywords

• nonn

Comments

Column 2 of A262849.

Examples

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

Links

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

Crossrefs

Cf. A262849.

Programs

Mathematica

v = Select[Tuples[{0, 1}, 4], Mod[FromDigits[#, 2], 7] == 0 &];
a[n_] := a[n] = Length[Select[Tuples[v, n + 2], !AnyTrue[Transpose[#], Mod[FromDigits[#, 2], 7] == 0 &] &]];
Table[a[n], {n, 1, 10}] (* Robert P. P. McKone, Jun 09 2024 *)

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) +20*a(n-3) -68*a(n-4) +68*a(n-5) -162*a(n-6) +444*a(n-7) -444*a(n-8) +644*a(n-9) -1244*a(n-10) +1244*a(n-11) -1277*a(n-12) +1376*a(n-13) -1376*a(n-14) +1032*a(n-15).