A291071 -id:A291071 - cp's OEIS frontend

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

N. J. A. Sloane, Aug 18 2017

nonn

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.

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

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 *)

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

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

A291070 Number of 4 X n binary matrices that are "primitive"; that is, they cannot be expressed as a "tiling" by a smaller matrix.

Original entry on oeis.org

30, 990, 32730, 1047540, 33554370, 1073708010, 34359738210, 1099510578960, 35184372055560, 1125899873286210, 36028797018961890, 1152921503532053580, 36893488147419095010, 1180591620683051547810, 37778931862957128089670, 1208925819613529663013120

Offset: 1

N. J. A. Sloane, Aug 18 2017

nonn

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.

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

Psi[k_, m_, n_] := Sum[MoebiusMu[dm] MoebiusMu[dn] k^(m n/dm/dn), {dm, Divisors[m] }, {dn, Divisors[n]}];
Table[Psi[2, 5, n], {n, 1, 16}] (* Jean-François Alcover, Aug 09 2018, after Lars Blomberg *)

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(16,n,Psi(2,5,n)) \\ Lars Blomberg, Aug 19 2017

a(8)-a(16) from Lars Blomberg, Aug 19 2017

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions