OFFSET
1,1
COMMENTS
Given the name of A054747, another name for this sequence can be "Number of inequivalent n-state 2-input 2-output connected automata with respect to an input permutation." - Petros Hadjicostas, Mar 08 2021
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
Christian G. Bower, PARI programs for transforms, 2007.
Michael A. Harrison, A census of finite automata, Canad. J. Math., 17, No. 1, (1965), 100-113. [First apply Theorem 6.2 (p. 107) with k = p = 2 to get A054747. Then apply Theorem 7.2 (p. 110) to get the number of classes of connected automata counted by A054747. - Petros Hadjicostas, Mar 08 2021]
N. J. A. Sloane, Maple programs for transforms, 2001-2020.
FORMULA
Inverse Euler transform of A054747. - Petros Hadjicostas, Mar 08 2021
PROG
(PARI) /* This program is a modification of Christian G. Bower's PARI program for the inverse Euler transform from the link above. */
lista(nn) = {local(A=vector(nn+1)); for(n=1, nn+1, A[n]=if(n==1, 1, A054747(n-1))); local(B=vector(#A-1, n, 1/n), C); A[1] = 1; C = log(Ser(A)); A=vecextract(A, "2.."); for(i=1, #A, A[i] = polcoeff(C, i)); A = dirdiv(A, B); } \\ Petros Hadjicostas, Mar 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Apr 22 2000
Terms a(14)-a(16) from Petros Hadjicostas, Mar 08 2021
STATUS
approved