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A290360
Number of 6-leaf rooted trees with n levels.
2
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
0,3
LINKS
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.
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.
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 *)
CROSSREFS
Row n=6 of A290353.
Sequence in context: A211921 A211795 A256226 * A359719 A356039 A073720
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jul 28 2017
STATUS
approved