0,2

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

Numbers whose base 4 representation consists entirely of 2's; twice base 4 repunits. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 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 (se16(AT)btinternet.com), 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 (deutsch(AT)duke.poly.edu), May 26 2003

a(n) = A007583(n+1)-1 = A039301(n+2)-2 = A083584(n)+1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 14 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 (reinhard.zumkeller(AT)gmail.com), 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 (deutsch(AT)duke.poly.edu), Apr 01 2004

Comment from Paul Barry, May 18, 2003: 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

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

Index entries for sequences related to linear recurrences with constant coefficients

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

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

G.f.: 2x/((1-x)(1-4x)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2008]

with(finance):seq(add(futurevalue(2, 3, k), k=0..n), n=-1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008

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

a(n) = A026644(2n)

a(n) = 2*A002450(n).

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

Cf. A020989.

Sequence in context: A085224 A024483 A084180 this_sequence A084480 A099553 A119694

Adjacent sequences: A020985 A020986 A020987 this_sequence A020989 A020990 A020991

nonn

N. J. A. Sloane (njas(AT)research.att.com).

Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 06 2006