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A036437
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Triangle of coefficients of generating function of ternary rooted trees of height exactly n.
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13
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1, 1, 1, 1, 1, 2, 4, 4, 5, 4, 4, 3, 2, 1, 1, 1, 3, 8, 15, 27, 43, 67, 97, 136, 183, 239, 300, 369, 432, 498, 551, 594, 614, 624, 601, 570, 514, 453, 378, 312, 238, 181, 128, 89, 56, 37, 20, 12, 6, 3, 1, 1, 1, 4, 13, 32, 74, 155, 316, 612, 1160, 2126, 3829, 6737
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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REFERENCES
| A. T. Balaban, J. W. Kennedy and L. V. Quintas, The number of alkanes having n carbons and a longest chain of length d, J. Chem. Education, 65 (No. 4, 1988), 304-313.
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LINKS
| Alois P. Heinz, Rows n = 1..8, flattened
Index entries for sequences related to rooted trees
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FORMULA
| T_{n}(z) - T_{n-1}(z) (see A036370).
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EXAMPLE
| 1;
1, 1, 1;
1, 2, 4, 4, 5, 4, 4, 3, 2, 1, 1;
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MAPLE
| df:= (t, l)-> zip((x, y)->x-y, t, l, 0):
T:= proc(n) option remember; local f, g;
if n=0 then 1
else f:= z-> add([T(n-1)][i]*z^(i-1), i=1..nops([T(n-1)]));
g:= expand (1 +z*(f(z)^3/6 +f(z^2)*f(z)/2 +f(z^3)/3));
seq (coeff (g, z, i), i=0..degree(g, z))
fi
end:
seq (df([T(n)], [T(n-1)])[n+1..-1][], n=1..5); # Alois P. Heinz, Sep 26 2011
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CROSSREFS
| Sequence in context: A009292 A009622 A036443 * A053306 A108422 A084616
Adjacent sequences: A036434 A036435 A036436 * A036438 A036439 A036440
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KEYWORD
| nonn,easy,tabf
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Eric Rains (rains(AT)caltech.edu)
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