A240801 - OEIS

A240801

Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = number of possible topologies with n given vertices and n-k-2 Steiner points.

%I #12 Jun 01 2024 05:38:22

%S 1,1,3,3,12,12,15,75,120,60,105,630,1350,1200,360,945,6615,17640,

%T 22050,12600,2520

%N Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = number of possible topologies with n given vertices and n-k-2 Steiner points.

%H E. N. Gilbert and H. O. Pollak, <a href="https://doi.org/10.1137/0116001">Steiner minimal trees</a>, SIAM J. Appl. Math. 16, (1968), pp. 1-29. See Table 1.

%e Triangle begins:

%e 1

%e 1, 3

%e 3, 12, 12

%e 15, 75, 120, 60

%e 105, 630, 1350, 1200, 360

%e 945, 6615, 17640, 22050, 12600, 2520

%e ...

%Y Row sums = A104653. A001710 and A001147 are diagonals.

%K nonn,tabl,more

%O 2,3

%A _N. J. A. Sloane_, Apr 13 2014