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A005193
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Balanced labeled graphs.
(Formerly M1231)
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0
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OFFSET
| 1,2
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COMMENTS
| Fuks and Sullivan give the formula as equation 26 on p. 6, the value a(10) and demonstrate that there exists a one-to-one correspondance between number-conserving two-input CA rules with n states and balanced sequences (to represent properly labeled balanced graphs) of length n. They also show with Stirling's approximation that a(n) is asymptotically bounded above by n^n^2. - Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 13 2007
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REFERENCES
| Sheppard, David A.; The factorial representation of balanced labeled graphs. Discrete Math. 15 (1976), no. 4, 379-388.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Henryk Fuks, Kate Sullivan, Enumeration of number-conserving cellular automata rules with two inputs, Nov 9, 2007; Journal of Cellular Automata 2 vol. 2 pp. 141-148 (2007).
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FORMULA
| If n is even: a(n) = 2*SUM[j=1..(n/2)] ((j!)^2)*j^(n-2*j). If n is odd: a(n) = 2*SUM[j=1..(n/2)] ((j!)^2)*j^(n-2*j) + ((n+1)/2)!*((n-1)/2)!. - Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 13 2007
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CROSSREFS
| Cf. A034384.
Sequence in context: A050397 A186021 A091174 * A173940 A101901 A124384
Adjacent sequences: A005190 A005191 A005192 * A005194 A005195 A005196
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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