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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112031 Numerator of 3/4 + 1/4 - 3/8 - 1/8 + 3/16 + 1/16 - 3/32 - 1/32 + 3/64 + .... 5
3, 1, 5, 1, 11, 3, 21, 5, 43, 11, 85, 21, 171, 43, 341, 85, 683, 171, 1365, 341, 2731, 683, 5461, 1365, 10923, 2731, 21845, 5461, 43691, 10923, 87381, 21845, 174763, 43691, 349525, 87381, 699051, 174763, 1398101, 349525, 2796203, 699051, 5592405 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Numerator of partial sums of A112030(n)/A016116(n+4), denominators = A112032;

a(n)/A112032(n) - 2/3 = (-1)^floor(n/2) / A112033(n);

a(n)/A112032(n) ---> 2/3.

REFERENCES

G. Polya and G. Szego, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chap. 4, Sect. 1, Problem 148

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

FORMULA

a(n) = (2^(floor(n/2) + 2 + (-1)^n) + (-1)^floor(n/2)) / 3.

Conjectures from Colin Barker, Apr 05 2013: (Start)

a(n) = a(n-2) + 2*a(n-4);

g.f.: (2*x^2+x+3) / ((1+x^2)*(1-2*x^2)). (End)

MATHEMATICA

LinearRecurrence[{0, 1, 0, 2}, {3, 1, 5, 1}, 50] (* Harvey P. Dale, Dec 31 2017 *)

PROG

(MAGMA) [(2^(Floor(n/2) + 2 + (-1)^n) + (-1)^Floor(n/2)) / 3: n in [0..50]]; // Vincenzo Librandi, Aug 17 2011

(PARI) m=50; v=concat([3, 1, 5, 1], vector(m-4)); for(n=5, m, v[n]=v[n-2] +2*v[n-4]); v \\ G. C. Greubel, Nov 08 2018

CROSSREFS

Cf. A016116, A112030, A112032, A112033.

Sequence in context: A126213 A146935 A133730 * A146285 A146059 A046531

Adjacent sequences:  A112028 A112029 A112030 * A112032 A112033 A112034

KEYWORD

nonn,frac

AUTHOR

Reinhard Zumkeller, Aug 27 2005

EXTENSIONS

Corrected a(22) by Vincenzo Librandi, Aug 17 2011

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 22 10:18 EDT 2019. Contains 322330 sequences. (Running on oeis4.)