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A006223
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Number of binary rooted trees of height n requiring 3 registers.
(Formerly M4940)
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1
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1, 14, 118, 780, 4466, 23276, 113620, 528840, 2375100, 10378056, 44381832, 186574864, 773564328, 3171317360, 12880883408, 51915526432, 207893871472, 827983736608
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OFFSET
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7,2
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COMMENTS
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The eighteen listed terms a(7)...a(24) satisfy a(n) = 14a(n-1) - 78a(n-2) + 220a(n-3) - 330a(n-4) + 252a(n-5) - 84a(n-6) + 8a(n-7) for n>7 (taking a(1), a(2), ..., a(6) = 0). - John W. Layman, Oct 14 1999
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=7..24.
P. Flajolet, J.-C. Raoult, and J. Vuillemin, The number of registers required for evaluating arithmetic expressions, Theoret. Comput. Sci. 9 (1979), no. 1, 99-125.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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MAPLE
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A006223:=-1/(2*z-1)/(2*z**4-16*z**3+20*z**2-8*z+1)/(2*z**2-4*z+1); # conjectured (correctly) by Simon Plouffe in his 1992 dissertation
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MATHEMATICA
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CoefficientList[-1/(2z - 1)/(2z^4 - 16z^3 + 20z^2 - 8z + 1)/(2z^2 - 4z + 1) + O[z]^18, z] (* Jean-François Alcover, Jul 29 2018, after Simon Plouffe *)
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CROSSREFS
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Sequence in context: A128569 A138431 A175874 * A091303 A241463 A284766
Adjacent sequences: A006220 A006221 A006222 * A006224 A006225 A006226
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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