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Search: id:A054745
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| A054745 |
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Number of nonisomorphic binary n-state automata without output under input permutations. |
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7
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| 1, 7, 74, 1474, 41876, 1540696, 68343112, 3540691525, 209612916303, 13957423192794, 1032436318269648, 83993175608894096, 7453446303042245261, 716451740543945788671, 74159075140708644544128
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also isomorphism classes of unordered pairs of endofunctions i.e. an unorder pair {f,g} of functions from {1,...,n} to itself. - Christian G. Bower (bowerc(AT)usa.net), Dec 18 2003
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REFERENCES
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M. A. Harrison, A census of finite automata, Canad. J. Math., 17, No. 1, 1965, p. 110.
F. Harary and E. Palmer, Graphical Enumeration, 1973.
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FORMULA
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a(n) = sum {1*s_1+2*s_2+...=n, 1*t_1+2*t_2=2} (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[...] = prod {i, j>=1} ( (sum {d|lcm(i, j)} (d*s_d))^(gcd(i, j)*s_i*t_j)) - Christian G. Bower (bowerc(AT)usa.net), Dec 18 2003
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CROSSREFS
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Cf. A001372, A054050, A054732, A054746.
Sequence in context: A000901 A098118 A097821 this_sequence A106162 A157706 A127190
Adjacent sequences: A054742 A054743 A054744 this_sequence A054746 A054747 A054748
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 22 2000
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