1,2

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 (jvospost2(AT)yahoo.com), Nov 13 2007

Sheppard, David A.; The factorial representation of balanced labeled graphs. Discrete Math. 15 (1976), no. 4, 379-388.

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).

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 (jvospost2(AT)yahoo.com), Nov 13 2007

Cf. A034384.

Sequence in context: A112846 A050397 A091174 this_sequence A101901 A124384 A001647

Adjacent sequences: A005190 A005191 A005192 this_sequence A005194 A005195 A005196

nonn

njas