A064455 a(2n) = 3n, a(2n-1) = n.

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

Offset

1,2

Comments

Also number of 1's in n-th row of triangle in A071030. - Hans Havermann, May 26 2002

Number of ON cells at generation n of 1-D 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(n-1) 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), 601--644.

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) / ( (x-1)^2*(1+x)^2 ). - R. J. Mathar, Mar 30 2011

From Jaroslav Krizek, Mar 22 2011: (Start)

a(n) = n - A123684(n-1) for odd n.

a(n) = n + a(n-1) 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^2-3n+2) mod (2n-1) for n>2. - Jim Singh, Oct 31 2018

Example

a(13) = a(2*7 - 1) = 7, a(14) = a(2*7) = 21.
a(8) = 8-9+10-11+12-13+14-15+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*n-1, ((n-1)*(n-2))%(2*n-1)) \\ 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: A245676 A341516 A060992 * A141619 A270143 A363278

Adjacent sequences: A064452 A064453 A064454 * A064456 A064457 A064458

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 02 2001

Status

approved