A263446 - OEIS

%I #48 May 02 2016 08:43:01

%S 1,1,3,1,7,12,6,52,119,137,195,231,1019,3503,6593,12616,26178,43500,

%T 64157,94688,232560,817757,2233757,5179734,11676838,24867480,50465099,

%U 99805751,190508209,357754875,668570596,1222920865,2191602460,4084023494,8885049152,22455345964,58818546941,151893212037,381199862655

%N Intervals of balanced binary trees in the Tamari lattices.

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

%H Joerg Arndt, <a href="/A263446/b263446.txt">Table of n, a(n) for n = 1..1000</a>

%H S. Giraudo, <a href="http://arxiv.org/abs/1107.3472">Intervals of balanced binary trees in the Tamari lattice</a>, arXiv preprint arXiv:1107.3472 [math.CO], 2011.

%H S. Giraudo, <a href="http://dx.doi.org/10.1016/j.tcs.2011.11.020">Intervals of balanced binary trees in the Tamari lattice</a>, Theoretical Computer Science, 420, 1--27, 2012.

%F 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).

%o (PARI) N = 66;  R = O('x^(N+1));  x = 'x+R;

%o 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) );

%o Vec( B(x,0,0) ) \\ _Joerg Arndt_, May 01 2016

%K nonn

%O 1,3

%A _Samuele Giraudo_, Apr 27 2016

%E Terms a(26) and beyond from _Joerg Arndt_, May 01 2016