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A061418 a(n) = floor(a(n-1)*3/2) with a(1) = 2.

%I A061418 #87 Aug 11 2025 20:59:21
%S A061418 2,3,4,6,9,13,19,28,42,63,94,141,211,316,474,711,1066,1599,2398,3597,
%T A061418 5395,8092,12138,18207,27310,40965,61447,92170,138255,207382,311073,
%U A061418 466609,699913,1049869,1574803,2362204,3543306,5314959,7972438
%N A061418 a(n) = floor(a(n-1)*3/2) with a(1) = 2.
%C A061418 Can be stated as the number of animals starting from a single pair if any pair of animals can produce a single offspring (as in the game Minecraft, if the player allows offspring to fully grow before breeding again). - _Denis Moskowitz_, Dec 05 2012
%C A061418 Maximum number of partial products that can be added in a Wallace tree multiplier with n-1 full adder stages. - _Chinmaya Dash_, Aug 19 2020
%H A061418 Iain Fox, <a href="/A061418/b061418.txt">Table of n, a(n) for n = 1..1000</a> (first 500 terms from Harry J. Smith)
%H A061418 Don Knuth, <a href="http://cs.stanford.edu/~knuth/papers/ambidextrous.pdf">Ambidextrous Numbers</a>, Preprint, September 2022.
%H A061418 M. van de Vel, <a href="http://www.emis.de/journals/JACO/Volume9_2/g618g3480371x5m8.html">Determination of msd(L^n)</a>, J. Algebraic Combin. 9(2) (1999), 161-171. See Table 5. - _N. J. A. Sloane_, Mar 26 2012
%H A061418 Mark van Wijk, <a href="http://essay.utwente.nl/91694/1/van%20Wijk_BA_EEMCS.pdf">The Quest for the Best Thread-Safe Java List</a>, Univ. of Twente (Netherlands 2022).
%H A061418 Wikipedia, <a href="https://en.wikipedia.org/wiki/Wallace_tree">Wallace tree</a>.
%F A061418 a(n) = A061419(n) + 1 = ceiling(K*(3/2)^n) where K = 1.08151366859...
%F A061418 The constant K is (2/3)*K(3) (see A083286). - _Ralf Stephan_, May 29 2003
%e A061418 a(6) = floor(9*3/2) = 13.
%o A061418 (Magma) [ n eq 1 select 2 else Floor(Self(n-1)*(3/2)): n in [1..39] ]; // _Klaus Brockhaus_, Nov 14 2008
%o A061418 (PARI) { a=4/3; for (n=1, 500, a=a*3\2; write("b061418.txt", n, " ", a) ) } \\ _Harry J. Smith_, Jul 22 2009
%o A061418 (PARI) first(n) = my(v=vector(n)); v[1]=2; for(i=2, n, v[i]=v[i-1]*3\2); v \\ _Iain Fox_, Jul 15 2022
%o A061418 (Python)
%o A061418 from itertools import islice
%o A061418 def A061418_gen(): # generator of terms
%o A061418     a = 2
%o A061418     while True:
%o A061418         yield a
%o A061418         a += a>>1
%o A061418 A061418_list = list(islice(A061418_gen(),70)) # _Chai Wah Wu_, Sep 20 2022
%Y A061418 Cf. A002379, A003312, A034082, A061419, A083286.
%Y A061418 First differences are in A073941.
%K A061418 nonn,easy
%O A061418 1,1
%A A061418 _Henry Bottomley_, May 02 2001