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A255637
Number of n-node rooted trees with a forbidden limb of length 7.
2
1, 1, 2, 4, 9, 20, 48, 114, 284, 714, 1829, 4731, 12391, 32711, 87084, 233349, 629137, 1705039, 4642999, 12696374, 34851662, 95997401, 265253845, 735035099, 2042203194, 5687771773, 15876641362, 44409566681, 124460776515, 349437246152, 982732274507
OFFSET
1,3
COMMENTS
Any rootward 7-node path starting at a leaf contains the root or a branching node.
LINKS
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 2.954528470057707474794966340476752099204837575... and c = 0.43932847920704393138249966062251759371... . - Vaclav Kotesovec, Feb 28 2016
MAPLE
g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
`if`(d=k, 1, 0)), d=divisors(j))*g(n-j, k), j=1..n)/n)
end:
a:= n-> g(n-1, 7):
seq(a(n), n=1..40);
CROSSREFS
Column k=7 of A255636.
Sequence in context: A036722 A318800 A318853 * A215796 A034824 A145545
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 28 2015
STATUS
approved