cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A291071 Number of 5 X n binary matrices that are "primitive"; that is, they cannot be expressed as a "tiling" by a smaller matrix.

This page as a plain text file.
%I A291071 #16 Aug 10 2018 02:38:00
%S A291071 54,3966,261522,16768860,1073708010,68718945018,4398044397642,
%T A291071 281474943095280,18014398374741048,1152921502458345570,
%U A291071 73786976286244079562,4722366482732172984420,302231454903107470761930,19342813113825270435966978,1237940039285345088379356750
%N A291071 Number of 5 X n binary matrices that are "primitive"; that is, they cannot be expressed as a "tiling" by a smaller matrix.
%H A291071 Guilhem Gamard, Gwenaël Richomme, Jeffrey Shallit, Taylor J. Smith, <a href="https://arxiv.org/abs/1602.06915">Periodicity in rectangular arrays</a>, arXiv:1602.06915 [cs.DM], 2016; Information Processing Letters 118 (2017) 58-63. See Table 1.
%t A291071 Psi[k_, m_, n_] := Sum[MoebiusMu[dm] MoebiusMu[dn] k^(m n/dm/dn), {dm, Divisors[m] }, {dn, Divisors[n]}];
%t A291071 Table[Psi[2, 6, n], {n, 1, 15}] (* _Jean-François Alcover_, Aug 10 2018, after _Lars Blomberg_ *)
%o A291071 (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])));
%o A291071 vector(15,n,Psi(2,6,n)) \\ _Lars Blomberg_, Aug 19 2017
%Y A291071 Cf. A027375, A102536, A265627, A290754, A291070.
%K A291071 nonn
%O A291071 1,1
%A A291071 _N. J. A. Sloane_, Aug 18 2017
%E A291071 a(8)-a(15) from _Lars Blomberg_, Aug 19 2017