A006223 Number of binary rooted trees of height n requiring 3 registers. (Formerly M4940)

1, 14, 118, 780, 4466, 23276, 113620, 528840, 2375100, 10378056, 44381832, 186574864, 773564328, 3171317360, 12880883408, 51915526432, 207893871472, 827983736608

Offset

7,2

Comments

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

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

Maple

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

Mathematica

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 *)

Crossrefs

Sequence in context: A138431 A175874 A359184 * A091303 A241463 A284766

Adjacent sequences: A006220 A006221 A006222 * A006224 A006225 A006226

Keyword

nonn

Author

N. J. A. Sloane

Status

approved