login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A020988 (2/3)*(4^n-1). 40
0, 2, 10, 42, 170, 682, 2730, 10922, 43690, 174762, 699050, 2796202, 11184810, 44739242, 178956970, 715827882, 2863311530, 11453246122, 45812984490, 183251937962, 733007751850, 2932031007402, 11728124029610, 46912496118442 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numbers whose binary representations is 10, n times (see A163662(n) for n >= 1). - Alexandre Wajnberg, May 31 2005

Numbers whose base 4 representation consists entirely of 2's; twice base 4 repunits. - Franklin T. Adams-Watters, Mar 29 2006

Expected time to finish a random Tower of Hanoi problem with 2n disks using optimal moves, so (since 2n is even and A010684(2n)=1) a(n)=A060590(2n). - Henry Bottomley, Apr 05 2001

a(n)=number of derangements of [2n+3] with runs consisting of consecutive integers. E.g. a(1)=10 because the derangements of {1,2,3,4,5} with runs consisting of consecutive integers are 5|1234, 45|123, 345|12, 2345|1, 5|4|123, 5|34|12, 45|23|1, 345|2|1, 5|4|23|1, 5|34|2|1 (the bars delimit the runs). - Emeric Deutsch, May 26 2003

For n>0 also smallest numbers having in binary representation exactly n+1 maximal groups of consecutive zeros: A087120(n)=a(n-1), see A087116. - Reinhard Zumkeller, Aug 14 2003

Number of walks of length 2n+3 between any two diametrically opposite vertices of the cycle graph C_6. Example: a(0)=2 because in the cycle ABCDEF we have two walks of length 3 between A and D: ABCD and AFED. - Emeric Deutsch, Apr 01 2004

From Paul Barry, May 18 2003: (Start)

Row sums of triangle using cumulative sums of odd-indexed rows of Pascal's triangle (start with zeros for completeness):

. . . . 0 . 0

. . . . 1 . 1

. . . 1 4 . 4 1

. . 1 6 14 14 6 1

.1 8 27 49 49 27 8 1  (End).

a(n) gives the position of the n-th zero in A173732, i.e. A173732(a(n))=0 for all n and this gives all the zeros in A173732. [Howard A. Landman, Mar 14 2010]

Smallest number having alternating bit sum -n. Cf. A065359.  For n=0,1,..., the last digit of a(n) is 0,2,0,2,... . - Washington Bomfim, Jan 22 2011

Number of toothpicks minus 1 in the toothpick structure of A139250 after 2^n stages. - Omar E. Pol, Mar 15 2012

For n>0 also partial sums of the odd powers of 2 (A004171). - K. G. Stier, Nov 04 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..170

J. Brillhart and P. Morton, A case study in mathematical research: the Golay-Rudin-Shapiro sequence, Amer. Math. Monthly, 103 (1996) 854-869.

Index to sequences with linear recurrences with constant coefficients, signature (5,-4).

FORMULA

a(n) = 4a(n-1) + 2, a(0)=0.

E.g.f. : (2/3)(exp(4x)-exp(x)). - Paul Barry, May 18 2003

a(n) = A007583(n+1)-1 = A039301(n+2)-2 = A083584(n)+1. - Ralf Stephan, Jun 14 2003

G.f.: 2x/((1-x)(1-4x)). [R. J. Mathar, Sep 17 2008]

a(n) = a(n-1) + 2^(2n-1), a(0) = 0. - Washington Bomfim, Jan 22 2011

a(n) = A193652(2*n). [Reinhard Zumkeller, Aug 08 2011]

a(n) = 5*a(n-1) - 4*a(n-2) (n>1), a(0)=0, a(1)=2. - L. Edson Jeffery, Mar 02 2012

a(n) = (2/3)*A024036(n). - Omar E. Pol, Mar 15 2012

MATHEMATICA

Table[ FromDigits[ Flatten[ Table[{1, 0}, {i, n}]], 2], {n, 0, 23}] (* Robert G. Wilson v, Jun 01 2005 *)

(2(4^Range[0, 30]-1))/3 (* or *) LinearRecurrence[{5, -4}, {0, 2}, 30] (* Harvey P. Dale, Sep 25 2013 *)

PROG

(PARI) an=0; print1(an, ", "); for(n=1, 23, an+=2^(2*n-1); print1(an, ", ")) \\ Washington Bomfim, Jan 22 2011

(MAGMA) [(2/3)*(4^n-1): n in [0..40] ]; // Vincenzo Librandi, Apr 28 2011

CROSSREFS

a(n) = A026644(2n).

a(n) = 2*A002450(n). These two sequences are both subsets of A000975.

a(n) = A007583(n)-1 = A039301(n+1)-2 = A083584(n-1)+1.

Cf. A020989.

Sequence in context: A181052 A024483 A084180 * A177238 A084480 A099553

Adjacent sequences:  A020985 A020986 A020987 * A020989 A020990 A020991

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Edited by N. J. A. Sloane, Sep 06 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 25 18:32 EST 2014. Contains 250000 sequences.