

A064455


a(2n) = 3n, a(2n1) = n.


18



1, 3, 2, 6, 3, 9, 4, 12, 5, 15, 6, 18, 7, 21, 8, 24, 9, 27, 10, 30, 11, 33, 12, 36, 13, 39, 14, 42, 15, 45, 16, 48, 17, 51, 18, 54, 19, 57, 20, 60, 21, 63, 22, 66, 23, 69, 24, 72, 25, 75, 26, 78, 27, 81, 28, 84, 29, 87, 30, 90, 31, 93, 32, 96, 33, 99, 34, 102, 35, 105, 36, 108
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Also number of 1's in nth row of triangle in A071030.  Hans Havermann, May 26 2002
Number of ON cells at generation n of 1D CA defined by Rule 54.  N. J. A. Sloane, Aug 09 2014
a(n)*A098557(n) equals the second right hand column of A167556.  Johannes W. Meijer, Nov 12 2009
Given a(1) = 1, for all n > 1, a(n) is the least positive integer not equal to a(n1) such that the arithmetic mean of the first n terms is an integer. The sequence of arithmetic means of the first 1, 2, 3, ..., terms is 1, 2, 2, 3, 3, 4, 4, ... (A004526 disregarding its first three terms).  Rick L. Shepherd, Aug 20 2013


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000
A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata with even rule numbers, 2016.
S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys., 55 (1983), 601644.
Index entries for linear recurrences with constant coefficients, signature (0,2,0,1)


FORMULA

a(n) = (1/2)*n*(1)^n + n + (1/4)*(1)^(n+1) + 1/4.  Stephen Crowley, Aug 10 2009
G.f.: x*(1+3*x) / ( (x1)^2*(1+x)^2 ).  R. J. Mathar, Mar 30 2011
From Jaroslav Krizek, Mar 22 2011: (Start)
a(n) = n  A123684(n1) for odd n.
a(n) = n + a(n1) for even n.
a(n) = A123684(n) + A137501(n).
Abs( a(n)  A123684(n) ) = A052928(n). (End)
a(n) = Sum_{i=n..2*n} i*(1)^i.  Bruno Berselli, Jun 05 2013
a(n) = n + floor(n/2)*(1)^(n mod 2).  Bruno Berselli, Dec 14 2015
a(n) = (n^23n+2) mod (2n1) for n>2.  Jim Singh, Oct 31 2018


EXAMPLE

a(13) = a(2*7  1) = 7, a(14) = a(2*7) = 21.
a(8) = 89+1011+1213+1415+16 = 12.  Bruno Berselli, Jun 05 2013


MAPLE

A064455 := proc(n)
if type(n, 'even') then
3*n/2 ;
else
(n+1)/2 ;
end if;
end proc: # R. J. Mathar, Aug 03 2015


MATHEMATICA

Table[ If[ EvenQ[n], 3n/2, (n + 1)/2], {n, 1, 70} ]


PROG

(ARIBAS): maxarg := 75; for n := 1 to maxarg do if n mod 2 = 1 then write((n+1) div 2, " ") else write((n div 2)*3, " "); end; end; .
(PARI) { for (n=1, 1000, if (n%2, a=(n + 1)/2, a=3*n/2); write("b064455.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 14 2009
(PARI) a(n)=if(n<3, 2*n1, ((n1)*(n2))%(2*n1)) \\ Jim Singh, Oct 14 2018
(Haskell)
import Data.List (transpose)
a064455 n = n + if m == 0 then n' else  n' where (n', m) = divMod n 2
a064455_list = concat $ transpose [[1 ..], [3, 6 ..]]
 Reinhard Zumkeller, Oct 12 2013
(MAGMA) [(1/2)*n*(1)^n+n+(1/4)*(1)^(n+1)+1/4: n in [1..80]]; // Vincenzo Librandi, Aug 10 2014
(GAP) a:=[];; for n in [1..75] do if n mod 2 = 0 then Add(a, 3*n/2); else Add(a, (n+1)/2); fi; od; a; # Muniru A Asiru, Oct 28 2018


CROSSREFS

Interleaving of A000027 and A008585 (without first term).
Cf. A064433, A071030, A080512, A225144, A265888.
Sequence in context: A038572 A245676 A060992 * A141619 A270143 A065021
Adjacent sequences: A064452 A064453 A064454 * A064456 A064457 A064458


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Oct 02 2001


STATUS

approved



