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A263446
Intervals of balanced binary trees in the Tamari lattices.
3
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
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
KEYWORD
nonn
AUTHOR
Samuele Giraudo, Apr 27 2016
EXTENSIONS
Terms a(26) and beyond from Joerg Arndt, May 01 2016
STATUS
approved