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

1,1

Comments

Column 2 of A262849.

Links

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

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).

Example

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

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 *)

Crossrefs

Cf. A262849.

Sequence in context: A368757 A222308 A166812 * A166941 A086934 A009469

Adjacent sequences: A262841 A262842 A262843 * A262845 A262846 A262847

Keyword

nonn

Author

R. H. Hardin, Oct 03 2015

Status

approved