OFFSET
1,3
REFERENCES
R. C. Read, Some Enumeration Problems in Graph Theory. Ph.D. Dissertation, Department of Mathematics, Univ. London, 1958.
R. W. Robinson, personal communication.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
R. W. Robinson, Computer print-out, no date. Gives first 29 terms.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. W. Robinson, Table of n, a(n) for n = 1..29 (corrected by Michel Marcus, Jan 19 2019)
G.-B. Chae, E. M. Palmer, R. W. Robinson, Counting labeled general cubic graphs, Discr. Math. 307 (2007) 2979-2992, eqs. (23) and (24).
R. W. Robinson, Cubic labeled graphs, computer print-out, n.d.
FORMULA
a(n) = (2*n)! * (s(n) - 2*s(n-1)) / (3*n*2^n) where s(1)=0, s(2)=1, and s(n) = 3*n*s(n-1) + 2*s(n-2) + (3*n-1) * Sum_{i=2..n-3} s(i) * s(n-1-i). - Sean A. Irvine, Oct 11 2017
MAPLE
s := proc(n)
option remember;
if n = 1 then
0;
elif n = 2 then
1;
else
3*n*procname(n-1)+2*procname(n-2)+(3*n-1)*add(procname(i)*procname(n-1-i), i=2..n-3) ;
end if;
end proc:
A007099 := proc(n)
if n = 1 then
0;
elif n = 2 then
1;
else
(2*n)!/3/n/2^n*(s(n)-2*s(n-1)) ;
end if;
end proc: # R. J. Mathar, Nov 08 2018
MATHEMATICA
s[n_] := s[n] = If[n <= 2, n - 1, 3 n s[n - 1] + 2 s[n - 2] + (3 n - 1) Sum[s[i] s[n - 1 - i], {i, 2, n - 3}]]; Array[Floor[(2 #)!*(s[#] - 2 s[# - 1])/(3 # 2^#)] &, 12] (* Michael De Vlieger, Oct 11 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved