%I #21 Mar 06 2016 19:23:02

%S 0,14,106,598,3002,14142,64106,283166,1228346,5257966,22281738,

%T 93689246,391512666,1627925006,6741353258,27821715326,114493140090,

%U 470023545198,1925545015370,7874137194718,32148981709466,131077794504654,533774656417642,2171261671337534,8823512782678714,35825200435380270

%N Let C(n) be the expected length of the longest carry chain when two n-bit binary numbers are added; sequence gives a(n) = 2^(2n-1)*C(n).

%C The addition is carried out by a parallel adder as described by J. von Neumann.

%H Volker Claus, <a href="http://dx.doi.org/10.1007/BF00289501">Die mittlere Additionsdauer eines Paralleladdierwerks</a>, Acta Informat. 2 (1973), 283-291.

%H D. E. Knuth, <a href="http://dx.doi.org/10.1016/1385-7258(78)90041-0">The average time for carry propagation</a>, Nederl. Akad. Wetensch. Indag. Math., 81 (2) (1978), 238-242.

%H Nicholas Pippenger, <a href="http://dx.doi.org/10.1006/jagm.2002.1216">Analysis of carry propagation in addition: an elementary approach</a>, J. Algorithms 42 (2002), 317-333.

%F C(n) = E(n)-1, where E(n) is defined in A190866.

%e C(n) for n >= 2: 0, 7/16, 53/64, 299/256, 1501/1024, 7071/4096, 32053/16384, 141583/65536, ...

%p See A190866.

%Y Cf. A190866.

%K nonn,frac

%O 2,2

%A _R. J. Mathar_ and _N. J. A. Sloane_, May 22 2011