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 A290754 Number of 3 X n binary matrices that are "primitive"; that is, they cannot be expressed as a "tiling" by a smaller matrix. 3
 12, 228, 4020, 65040, 1047540, 16768860, 268419060, 4294836480, 68719210560, 1099509531420, 17592181850100, 281474943095280, 4503599560261620, 72057593501073180, 1152921503532053580, 18446744065119682560, 295147905162172956660, 4722366482732189753280 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 18 11:52 EDT 2024. Contains 371779 sequences. (Running on oeis4.)