A395475 Number of 3 X n binary matrices that are "primitive"; that is, they cannot be expressed as a "tiling" by a smaller matrix.

6, 54, 498, 4020, 32730, 261522, 2097018, 16772880, 134216712, 1073708010, 8589932538, 68719206540, 549755805690, 4398044397642, 35184372022830, 281474959868160, 2251799813554170, 18014398374741048, 144115188075331578, 1152921503532053580, 9223372036850581134

Offset

1,1

Links

Table of n, a(n) for n=1..21.

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).

Formula

a(n) = A323862(n, 3). - Rémy Sigrist, Apr 30 2026

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, 3, n)) \\ Sean A. Irvine, Apr 29 2026 (after Lars Blomberg)

Crossrefs

Cf. A027375, A102536, A265627, A290754, A291070, A291071, A323862.

Sequence in context: A177484 A353207 A092810 * A092472 A228413 A098658

Adjacent sequences: A395472 A395473 A395474 * A395476 A395477 A395478

Keyword

nonn

Author

Taylor J. Smith, Apr 24 2026

Extensions

More terms from Sean A. Irvine, Apr 29 2026

Status

approved