A290754 Number of 3 X n binary matrices that are "primitive"; that is, they cannot be expressed as a "tiling" by a smaller matrix.

12, 228, 4020, 65040, 1047540, 16768860, 268419060, 4294836480, 68719210560, 1099509531420, 17592181850100, 281474943095280, 4503599560261620, 72057593501073180, 1152921503532053580, 18446744065119682560, 295147905162172956660, 4722366482732189753280

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Guilhem Gamard, Gwenaël Richomme, Jeffrey Shallit, Taylor J. Smith, Periodicity in rectangular arrays, arXiv:1602.06915 [cs.DM], 2016; Information Processing Letters 118 (2017) 58-63. See Table 1.

Mathematica

Psi[k_, m_, n_] := Sum[MoebiusMu[dm] MoebiusMu[dn] k^(m n/dm/dn), {dm, Divisors[m] }, {dn, Divisors[n]}];
Table[Psi[2, 4, n], {n, 1, 18}] (* Jean-François Alcover, Aug 09 2018, after Lars Blomberg *)

Prog

(PARI) Psi(k, m, n) = v1=divisors(m); v2=divisors(n); sum(i1=1, length(v1), sum(i2=1, length(v2), moebius(v1[i1])*moebius(v2[i2])*k^(m*n/v1[i1]/v2[i2])));
vector(18, n, Psi(2, 4, n)) \\ Lars Blomberg, Aug 19 2017

Crossrefs

Cf. A027375, A102536, A265627, A291070, A291071.

Sequence in context: A361184 A358362 A337332 * A318417 A034832 A231448

Adjacent sequences: A290751 A290752 A290753 * A290755 A290756 A290757

Keyword

nonn

Author

N. J. A. Sloane, Aug 18 2017

Extensions

a(8)-a(18) from Lars Blomberg, Aug 19 2017

Status

approved