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Search: id:A086193
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| A086193 |
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Number of n X n matrices with entries in {0,1} with no zero row, no zero column and with zero main diagonal. |
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+0
5
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| 0, 1, 18, 1699, 592260, 754179301, 3562635108438, 63770601591579079, 4405870283636411477640, 1190873924687350003735546441, 1270602397076493907445608866890778, 5381240610642043789096251476993474339179
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Also the number of simple labeled digraphs on n nodes for which every vertex has indegree at least one and outdegree at least one.
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FORMULA
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a(n) = sum( (-1)^(n-r)*binomial(n, r)*(2^(r-1)-1)^r*(2^r-1)^(n-r), r=0..n ). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 27 2003
a(n) = sum( f(n, r), r=0..n ) where f(n, r) = binomial(n, r) (-1)^r (1-2^(-n+r+1))^(n-r) (1-2^(-n+r))^r 2^((n-r)(n-1))
E.g.f.: Sum((2^(n-1)-1)^n*exp((1-2^n)*x)*x^n/n!,n=0..infinity). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 23 2008
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MATHEMATICA
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Table[ it = (Partition[ #1, n ] &) /@ IntegerDigits[ Range[ 0, -1 + 2^n^2 ], 2, n^2 ]; Count[ it, (q_)?MatrixQ /; Tr[ q ] === 0 && (Times @@ (Plus @@@ q)) > 0 && (Times @@ (Plus @@@ Transpose[ q ]) > 0) ], {n, 1, 4} ]
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CROSSREFS
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Sequence in context: A064564 A003030 A086366 this_sequence A064347 A067303 A055740
Adjacent sequences: A086190 A086191 A086192 this_sequence A086194 A086195 A086196
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KEYWORD
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nonn
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AUTHOR
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Edwin Clark (eclark(AT)math.usf.edu), Aug 25 2003
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EXTENSIONS
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Mathematica program from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 25 2003; formula and more terms from Brendan McKay, Aug 27, 2003
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