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A061418 a(n) = floor(a(n-1)*3/2) with a(1) = 2. 22
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 (list; graph; refs; listen; history; text; internal format)
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

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(2) (1999), 161-171. See Table 5. - N. J. A. Sloane, Mar 26 2012

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

CROSSREFS

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

First differences are in A073941.

Sequence in context: A101913 A121653 A238434 * A136423 A215245 A078932

Adjacent sequences:  A061415 A061416 A061417 * A061419 A061420 A061421

KEYWORD

nonn,changed

AUTHOR

Henry Bottomley, May 02 2001

STATUS

approved

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Last modified September 26 20:09 EDT 2020. Contains 337374 sequences. (Running on oeis4.)