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A263446
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Intervals of balanced binary trees in the Tamari lattices.
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3
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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
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OFFSET
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1,3
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COMMENTS
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a(n) is the number of intervals of balanced binary trees in the Tamari lattice of binary trees with n internal nodes.
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LINKS
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FORMULA
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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).
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PROG
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(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) );
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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