

A061418


a(n) = floor(a(n1)*3/2) with a(1) = 2.


20



2, 3, 4, 6, 9, 13, 19, 28, 42, 63, 94, 141, 211, 316, 474, 711, 1066, 1599, 2398, 3597, 5395, 8092, 12138, 18207, 27310, 40965, 61447, 92170, 138255, 207382, 311073, 466609, 699913, 1049869, 1574803, 2362204, 3543306, 5314959, 7972438
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OFFSET

1,1


COMMENTS

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


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..500
M. van de Vel, Determination of msd(L^n), J. Algebraic Combin., 9 (1999), 161171. See Table 5.  N. J. A. Sloane, Mar 26 2012


FORMULA

a(n) = A061419(n)+1 = ceiling(K*(3/2)^n) where K=1.08151366859...
The constant K is 2/3*K(3) (see A083286).  Ralf Stephan, May 29, 2003


EXAMPLE

a(6) = floor(9*3/2) = 13.


MATHEMATICA

lst = {}; s = 2; Do[s = Floor[s*1.5]; AppendTo[lst, s], {n, 1, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 13 2008 *)


PROG

(MAGMA) [ n eq 1 select 2 else Floor(Self(n1)*(3/2)): n in [1..39] ]; // Klaus Brockhaus, Nov 14 2008
(PARI) { a=4/3; for (n=1, 500, a=a*3\2; write("b061418.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 22 2009


CROSSREFS

Cf. A002379, A034082, A061419, A003312.
First differences are in A073941.
Sequence in context: A101913 A121653 A238434 * A136423 A215245 A078932
Adjacent sequences: A061415 A061416 A061417 * A061419 A061420 A061421


KEYWORD

nonn


AUTHOR

Henry Bottomley, May 02 2001


STATUS

approved



