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A060723 a(n) is the denominator of r(n) where r(n) is the sequence of rational numbers defined by the recursion: r(0) = 0, r(1) = 1 and for n>1 r(n) = r(n-1) + r(n-2)/2. From this definition it is clear that a(n) is always a power of 2 (see A060755). 2
1, 1, 1, 2, 1, 4, 4, 8, 1, 16, 16, 32, 8, 64, 64, 128, 8, 256, 256, 512, 128, 1024, 1024, 2048, 256, 4096, 4096, 8192, 2048, 16384, 16384, 32768, 1024, 65536, 65536, 131072, 32768, 262144, 262144, 524288, 65536, 1048576, 1048576, 2097152 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..43.

FORMULA

r(n) = (((1/2)*(sqrt(3) + 1))^n - ((1/2)*(sqrt(3) - 1))^n * cos(Pi*n))/sqrt(3). - Peter Luschny, Jun 02 2018

EXAMPLE

The sequence r(n) begins 0, 1, 1, 3/2, 2, 11/4, 15/4, 41/8, 7, 153/16, 209/16, 571/32, 363/16, 2023/64, 2749/64, 7521/128, 5135/64, ... It can be proved that r(n) is an integer (i.e. a(n) = 1) if and only if n is one of 0, 1, 2, 4, 8.

MATHEMATICA

Denominator[RecurrenceTable[{a[0]==0, a[1]==1, a[n]==a[n-1]+a[n-2]/2}, a, {n, 50}]] (* Harvey P. Dale, Mar 07 2016 *)

Table[Denominator[Simplify[((1/2(1 + Sqrt[3]))^x - (1/2(Sqrt[3] - 1))^x Cos[Pi x])/ Sqrt[3]]], {x, 0, 43}]  (* Peter Luschny, Jun 02 2018 *)

CROSSREFS

Cf. A060755, A305491 (numerators).

Sequence in context: A077967 A296188 A008312 * A300622 A195691 A074763

Adjacent sequences:  A060720 A060721 A060722 * A060724 A060725 A060726

KEYWORD

nonn,easy

AUTHOR

Avi Peretz (njk(AT)netvision.net.il), Apr 21 2001

EXTENSIONS

More terms from Vladeta Jovovic, Apr 24 2001

STATUS

approved

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Last modified January 22 07:30 EST 2020. Contains 331139 sequences. (Running on oeis4.)