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

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

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

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

Links

Iain Fox, Table of n, a(n) for n = 1..1000 (first 500 terms from Harry J. Smith)

Don Knuth, Ambidextrous Numbers, Preprint, September 2022.

M. van de Vel, Determination of msd(L^n), J. Algebraic Combin. 9(2) (1999), 161-171. See Table 5. - N. J. A. Sloane, Mar 26 2012

Mark van Wijk, The Quest for the Best Thread-Safe Java List, Univ. of Twente (Netherlands 2022).

Wikipedia, Wallace tree.

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.

Prog

(Magma) [ n eq 1 select 2 else Floor(Self(n-1)*(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
(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
(Python)
from itertools import islice
def A061418_gen(): # generator of terms
    a = 2
    while True:
        yield a
        a += a>>1
A061418_list = list(islice(A061418_gen(), 70)) # Chai Wah Wu, Sep 20 2022

Crossrefs

Cf. A002379, A003312, A034082, A061419, A083286.

First differences are in A073941.

Sequence in context: A352042 A121653 A238434 * A355909 A136423 A215245

Adjacent sequences: A061415 A061416 A061417 * A061419 A061420 A061421

Keyword

nonn,easy

Author

Henry Bottomley, May 02 2001

Status

approved