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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
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
Sequence in context: A361184 A358362 A337332 * A318417 A034832 A231448
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.)