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 A002724 Number of inequivalent n X n binary matrices, where equivalence means permutations of rows or columns. (Formerly M1801 N0711) 34
 1, 2, 7, 36, 317, 5624, 251610, 33642660, 14685630688, 21467043671008, 105735224248507784, 1764356230257807614296, 100455994644460412263071692, 19674097197480928600253198363072, 13363679231028322645152300040033513414, 31735555932041230032311939400670284689732948 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A diagonal of the array A(m,n) described in A028657. - N. J. A. Sloane, Sep 01 2013 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..26 A. Kerber, Experimentelle Mathematik, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 19 (1988), 77-83. [Annotated scanned copy] Math StackExchange, How many n-by-m binary matrices are there up to row and column permutations B. Misek, On the number of classes of strongly equivalent incidence matrices, (Czech with English summary) Casopis Pest. Mat. 89 1964 211-218. Marko Riedel, Maple code with two different algorithms M. Zivkovic, Classification of small (0,1) matrices, arXiv:math/0511636 [math.CO], 2005. FORMULA a(n) = sum {1*s_1+2*s_2+...=n, 1*t_1+2*t_2+...=n} (fix A[s_1, s_2, ...;t_1, t_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...*1^t_1*t_1!*2^t_2*t_2!*...)) where fix A[...] = 2^sum {i, j>=1} (gcd(i, j)*s_i*t_j). - Christian G. Bower, Dec 18 2003 MAPLE # See Marko Riedel link. MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, {0}, If[i < 1, {}, Union[Flatten[Table[ Function[{p}, p + j*x^i] /@ b[n - i*j, i - 1], {j, 0, n/i}]]]]]; g[n_, k_] := g[n, k] = Sum[Sum[2^Sum[Sum[GCD[i, j]*Coefficient[s, x, i]* Coefficient[t, x, j], {j, 1, Exponent[t, x]}], {i, 1, Exponent[s, x]}]/ Product[i^Coefficient[s, x, i]*Coefficient[s, x, i]!, {i, 1, Exponent[s, x]}]/Product[i^Coefficient[t, x, i]*Coefficient[t, x, i]!, {i, 1, Exponent[t, x]}], {t, b[n + k, n + k]}], {s, b[n, n]}]; A[n_, k_] := g[Min[n, k], Abs[n - k]]; Table[A[n, n], {n, 0, 15}] (* Jean-François Alcover, Aug 10 2018, after Alois P. Heinz *) CROSSREFS Cf. A002623, A002727, A006148, A002728, A002725, A052269, A052271, A052272, A091059. Cf. A028657 (this sequence is the diagonal). - N. J. A. Sloane, Sep 01 2013 Column k=2 of A246106. Sequence in context: A012717 A072236 A007474 * A292206 A203900 A209251 Adjacent sequences:  A002721 A002722 A002723 * A002725 A002726 A002727 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Feb 04 2000 a(15) from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 24 2008 Added Maple code to compute the cycle indices of the group permuting the slots of the matrix and hence the values of the sequence, Marko Riedel, Jul 27 2014 Added Maple implementation of the closed form result by C. G. Bower and of the textbook method, Marko Riedel, Jul 28 2014 Moved Maple code from inline to attachment by Marko Riedel, Dec 27 2014 STATUS approved

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Last modified May 25 01:37 EDT 2019. Contains 323534 sequences. (Running on oeis4.)