A290360 Number of 6-leaf rooted trees with n levels.

0, 1, 11, 58, 206, 571, 1337, 2772, 5244, 9237, 15367, 24398, 37258, 55055, 79093, 110888, 152184, 204969, 271491, 354274, 456134, 580195, 729905, 909052, 1121780, 1372605, 1666431, 2008566, 2404738, 2861111, 3384301, 3981392, 4659952, 5428049, 6294267

Offset: 0

Author

Alois P. Heinz, Jul 28 2017

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• B. A. Huberman and T. Hogg, Complexity and adaptation, Evolution, games and learning (Los Alamos, N.M., 1985). Phys. D 22 (1986), no. 1-3, 376-384.
• Index entries for sequences related to rooted trees
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Row n=6 of A290353.

Programs

Maple

a:= n-> ((((4*n+5)*n+10)*n+10)*n+1)*n/30:
seq(a(n), n=0..40);

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,11,58,206,571},40] (* Harvey P. Dale, Aug 22 2019 *)

Formula

G.f.: (3*x+1)*(x+1)^2*x / (x-1)^6.

a(n) = (4*n^5+5*n^4+10*n^3+10*n^2+n)/30.