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A301343
Regular triangle where T(n,k) is the number of planted achiral (or generalized Bethe) trees with n nodes and k leaves.
7
1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 3, 2, 2, 1, 1, 0, 1, 3, 2, 2, 1, 1, 1, 0, 1, 4, 2, 4, 1, 2, 1, 1, 0, 1, 4, 3, 4, 1, 3, 1, 1, 1, 0, 1, 5, 3, 6, 2, 4, 1, 2, 1, 1, 0, 1, 5, 3, 6, 2, 4, 1, 2, 1, 1, 1, 0, 1, 6, 4, 9, 2, 7, 1, 4, 2, 2, 1, 1, 0
OFFSET
1,12
FORMULA
T(n,1) = 1, T(n,k) = 0 if n <= k, otherwise T(n,k) = Sum_{d|k} T(n - k, d).
EXAMPLE
Triangle begins:
1
1 0
1 1 0
1 1 1 0
1 2 1 1 0
1 2 1 1 1 0
1 3 2 2 1 1 0
1 3 2 2 1 1 1 0
1 4 2 4 1 2 1 1 0
1 4 3 4 1 3 1 1 1 0
1 5 3 6 2 4 1 2 1 1 0
The T(9,4) = 4 planted achiral trees: (((((oooo))))), ((((oo)(oo)))), (((oo))((oo))), ((o)(o)(o)(o)).
MATHEMATICA
tri[n_, k_]:=If[k===1, 1, If[k>=n, 0, Sum[tri[n-k, d], {d, Divisors[k]}]]];
Table[tri[n, k], {n, 10}, {k, n}]
CROSSREFS
Row sums are A003238. A version without the zeroes or first row is A214575.
Sequence in context: A048825 A339884 A116375 * A353446 A054078 A029400
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Mar 19 2018
STATUS
approved