A006223 - OEIS

%I M4940 #32 Apr 13 2022 13:25:18

%S 1,14,118,780,4466,23276,113620,528840,2375100,10378056,44381832,

%T 186574864,773564328,3171317360,12880883408,51915526432,207893871472,

%U 827983736608

%N Number of binary rooted trees of height n requiring 3 registers.

%C 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

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

%H P. Flajolet, J.-C. Raoult, and J. Vuillemin, <a href="https://dx.doi.org/10.1016/0304-3975(79)90009-4">The number of registers required for evaluating arithmetic expressions</a>, Theoret. Comput. Sci. 9 (1979), no. 1, 99-125.

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%p 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

%t 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_ *)

%K nonn

%O 7,2

%A _N. J. A. Sloane_