OFFSET
1,3
COMMENTS
Let F(n,s) = number of Steiner trees with n vertices and s Steiner points; then A001147 is also F(n,n-2) for n>2. - Robert G. Wilson v, May 10 2005
LINKS
E. N. Gilbert and H. O. Pollak, Steiner minimal trees, SIAM J. Appl. Math. 16, (1968), pp. 1-29.
FORMULA
a(n) = Sum_{s=0..n-2} 2^(-s)*binomial(n, s+2)*(n+s-2)!/s!. - Robert G. Wilson v, May 10 2005
a(n) ~ 3^(3/4) * (2 + sqrt(3))^(n - 3/2) * n^(n-2) / exp(n). - Vaclav Kotesovec, Nov 27 2017
EXAMPLE
Let F(n,s) = number of Steiner trees with n vertices and s Steiner points. Then a(3)=4 because we can have F(3,0)=3 and F(3,1)=1.
MATHEMATICA
f[n_] := Sum[ Binomial[n, k + 2](n + k - 2)!/(k!2^k), {k, 0, n - 2}]; Table[ f[n], {n, 18}] (* Robert G. Wilson v, May 10 2005 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Alexandre Goncalves (alexg(AT)civil.ist.utl.pt), Apr 22 2005
EXTENSIONS
More terms from Robert G. Wilson v, May 10 2005
STATUS
approved