A263446 Intervals of balanced binary trees in the Tamari lattices.

1, 1, 3, 1, 7, 12, 6, 52, 119, 137, 195, 231, 1019, 3503, 6593, 12616, 26178, 43500, 64157, 94688, 232560, 817757, 2233757, 5179734, 11676838, 24867480, 50465099, 99805751, 190508209, 357754875, 668570596, 1222920865, 2191602460, 4084023494, 8885049152, 22455345964, 58818546941, 151893212037, 381199862655

Offset

1,3

Comments

a(n) is the number of intervals of balanced binary trees in the Tamari lattice of binary trees with n internal nodes.

Links

Joerg Arndt, Table of n, a(n) for n = 1..1000

S. Giraudo, Intervals of balanced binary trees in the Tamari lattice, arXiv preprint arXiv:1107.3472 [math.CO], 2011.

S. Giraudo, Intervals of balanced binary trees in the Tamari lattice, Theoretical Computer Science, 420, 1--27, 2012.

Formula

G.f.: A(x) = B(x, 0, 0) where B(x, y, z) satisfies B(x, y, z) = x + B(x^2 + 2*x*y + y*z, x, x^2 + x*y).

Prog

(PARI) N = 66;  R = O('x^(N+1));  x = 'x+R;
B(x, y, z, k=0) = if( k>=N, x, x + R + B(x^2 + 2*x*y + y*z + R,  x + R,  x^2 + x*y + R, k+1) );
Vec( B(x, 0, 0) ) \\ Joerg Arndt, May 01 2016

Crossrefs

Sequence in context: A232965 A249401 A196845 * A297192 A218592 A113647

Adjacent sequences: A263443 A263444 A263445 * A263447 A263448 A263449

Keyword

nonn

Author

Samuele Giraudo, Apr 27 2016

Extensions

Terms a(26) and beyond from Joerg Arndt, May 01 2016

Status

approved