A335562 Number of unlabelled unary-binary trees with n nodes such that every node with two children has children of different subtree sizes.

1, 1, 1, 3, 5, 13, 29, 71, 165, 421, 1029, 2647, 6593, 17241, 43801, 115555, 297513, 791337, 2062737, 5516755, 14497373, 38994597, 103269053, 278921927, 742950845, 2014648253, 5396210357, 14677306503, 39477832745, 107701409665, 290871580345, 795431700707, 2155140605137

Offset

1,4

Links

Table of n, a(n) for n=1..33.

Formula

a(1) = 1, a(n) = a(n-1) + Sum_{k=1..n-2} (a(k)*a(n-k-1)*[k != n-k-1]).

Prog

(PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = va[n-1] + sum(k=1, n-2, if (k != n-k-1, va[k]*va[n-k-1])); ); va; } \\ Michel Marcus, Jun 14 2020

Crossrefs

Cf. A000992.

Sequence in context: A067932 A339155 A168314 * A106666 A124791 A147046

Adjacent sequences: A335559 A335560 A335561 * A335563 A335564 A335565

Keyword

nonn

Author

Marcel K. Goh, Jun 14 2020

Status

approved