login
A301368
Regular triangle where T(n,k) is the number of binary enriched p-trees of weight n with k leaves.
9
1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 2, 4, 5, 3, 1, 3, 7, 12, 12, 6, 1, 3, 9, 19, 28, 25, 11, 1, 4, 14, 36, 65, 81, 63, 24, 1, 4, 16, 48, 107, 172, 193, 136, 47, 1, 5, 22, 75, 192, 369, 522, 522, 331, 103, 1, 5, 25, 96, 284, 643, 1108, 1420, 1292, 750, 214, 1, 6
OFFSET
1,8
COMMENTS
A binary enriched p-tree of weight n is either a single node of weight n, or an ordered pair of binary enriched p-trees with weakly decreasing weights summing to n.
LINKS
EXAMPLE
Triangle begins:
1
1 1
1 1 1
1 2 3 2
1 2 4 5 3
1 3 7 12 12 6
1 3 9 19 28 25 11
1 4 14 36 65 81 63 24
1 4 16 48 107 172 193 136 47
1 5 22 75 192 369 522 522 331 103
...
The T(6,3) = 7 binary enriched p-trees: ((41)1), ((32)1), (4(11)), ((31)2), ((22)2), (3(21)), ((21)3).
MATHEMATICA
bintrees[n_]:=Prepend[Join@@Table[Tuples[bintrees/@ptn], {ptn, Select[IntegerPartitions[n], Length[#]===2&]}], n];
Table[Length[Select[bintrees[n], Count[#, _Integer, {-1}]===k&]], {n, 13}, {k, n}]
PROG
(PARI) A(n)={my(v=vector(n)); for(n=1, n, v[n] = y + sum(k=1, n\2, v[k]*v[n-k])); apply(p->Vecrev(p/y), v)}
{ my(T=A(10)); for(n=1, #T, print(T[n])) } \\ Andrew Howroyd, Aug 26 2018
CROSSREFS
Last entries of each row give A000992. Row sums are A300443.
Sequence in context: A245436 A285581 A222173 * A198242 A049063 A120894
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Mar 19 2018
STATUS
approved