A291071 Number of 6 X n binary matrices that are "primitive"; that is, they cannot be expressed as a "tiling" by a smaller matrix.

54, 3966, 261522, 16768860, 1073708010, 68718945018, 4398044397642, 281474943095280, 18014398374741048, 1152921502458345570, 73786976286244079562, 4722366482732172984420, 302231454903107470761930, 19342813113825270435966978, 1237940039285345088379356750

Offset

1,1

Links

Table of n, a(n) for n=1..15.

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

Taylor J. Smith, Primitive Two-Dimensional Words and Iterated Pedal Triangles via Symbolic Coding, arXiv:2604.26832 [math.DS], 2026. See p. 5 (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, 6, n], {n, 1, 15}] (* Jean-François Alcover, Aug 10 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(15, n, Psi(2, 6, n)) \\ Lars Blomberg, Aug 19 2017

Crossrefs

Cf. A027375, A102536, A265627, A290754, A291070.

Sequence in context: A046199 A245831 A368366 * A254620 A299862 A342893

Adjacent sequences: A291068 A291069 A291070 * A291072 A291073 A291074

Keyword

nonn

Author

N. J. A. Sloane, Aug 18 2017

Extensions

a(8)-a(15) from Lars Blomberg, Aug 19 2017

Definition corrected by Taylor J. Smith, Apr 24 2026

Status

approved