|
|
A131891
|
|
a(n) is the number of shapes of balanced trees with constant branching factor 5 and n nodes. The node is balanced if the size, measured in nodes, of each pair of its children differ by at most one node.
|
|
6
|
|
|
1, 1, 5, 10, 10, 5, 1, 25, 250, 1250, 3125, 3125, 31250, 125000, 250000, 250000, 100000, 500000, 1000000, 1000000, 500000, 100000, 250000, 250000, 125000, 31250, 3125, 3125, 1250, 250, 25, 1, 125, 6250, 156250, 1953125, 9765625, 488281250, 9765625000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(0) = a(1) = 1; a(5n+1+m) = (5 choose m) * a(n+1)^m * a(n)^(5-m), where n >= 0 and 0 <= m <= 5.
|
|
MAPLE
|
a:= proc(n) option remember; local m, r; if n<2 then 1 else
r:= iquo(n-1, 5, 'm'); binomial(5, m) *a(r+1)^m *a(r)^(5-m) fi
end:
|
|
MATHEMATICA
|
a[n_, k_] := a[n, k] = Module[{m, r}, If[n < 2 || k == 1, 1, If[k == 0, 0, {r, m} = QuotientRemainder[n - 1, k]; Binomial[k, m]*a[r + 1, k]^m*a[r, k]^(k - m)]]];
a[n_] := a[n, 5];
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|