

A158618


Number of gates in LadnerFisher prefix circuit


0



0, 1, 2, 4, 5, 7, 9, 12, 13, 15, 17, 20, 22, 25, 27, 31, 32, 34, 36, 39, 41, 44, 46, 50, 52, 55, 57, 61, 64, 67, 69, 74, 75, 77, 79, 82, 84, 87, 89, 93
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OFFSET

1,3


REFERENCES

D.E. Knuth, The Art of Computer Programming, Volume 4, Fascicle 0. See exercise 7.1.2.36 and solution.
R.E. Ladner and M.J. Fischer, Parallel Prefix Computation, JACM 27 (1980) 831838.


LINKS

Table of n, a(n) for n=1..40.


FORMULA

With s = floor(n/2), r = ceiling(n/2) and a(1) = b(1) = 0,
recurrence relation is a(n) = s + b(r) + a(s), b(n) = 2s1 + a(r).
If n = 2^m then a(n) = 4n+1  Fibonacci(m+5).


CROSSREFS

Sequence in context: A140205 A140206 A007818 * A000788 A053039 A286753
Adjacent sequences: A158615 A158616 A158617 * A158619 A158620 A158621


KEYWORD

nonn


AUTHOR

Frank Ruskey, Mar 22 2009


STATUS

approved



