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
Andrew Howroyd, Table of n, a(n) for n = 1..1275
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
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Mar 19 2018
STATUS
approved