The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A232221 a(n) = Sum_{i=1..n} (A077068(i) - A077065(i)). 5
 0, 0, 4, 20, 36, 52, 128, 216, 328, 464, 636, 796, 908, 1092, 1324, 1520, 1716, 1948, 2144, 2436, 2716, 2972, 3264, 3580, 3812, 4032, 4168, 4268, 4416, 4720, 5012, 5328, 5716, 6128, 6504, 6700, 6932, 7248, 7684, 8180, 8676, 9268, 9680, 10140, 10624, 11024, 11400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The sequence has wild fluctuations - see the successive plots in the links. This is typical behavior for a particle whose movement is governed by an arc-sine law (cf. Feller, Chap. III). - N. J. A. Sloane, Nov 23 2013 Negative stretches: terms 941-1031 and 13197-1431205. - Hans Havermann, Nov 23 2013 After reaching a local maximum of 21957005755012 at term 24118371, the sequence again descends with the first negative of a third such stretch at term 32437583. - Hans Havermann, Nov 28 2013 All terms are multiples of 4, cf. A008586. - Reinhard Zumkeller, Nov 22 2013 See A232361 and A232359 for peak values and where they occur: max{a(A232359(n)-1), a(A232359(n)+1)} < a(A232359(n)) = A232361(n). - Reinhard Zumkeller, Nov 24 2013 REFERENCES W. Feller, An Introduction to Probability Theory and its Applications, 3rd ed, Wiley, New York, 1968. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 OEIS "graph" command, Pin plot of 200 terms, scatter plot of 10000 terms Hans Havermann, Four graphs with an increasing number of terms, personal web page. Veikko Pohjola, Re: Sister sequences, SeqFan list, Nov 22 2013. (Early observation on how the sequence evolves.) PROG (Haskell) a232221 n = a232221_list !! (n-1) a232221_list = scanl1 (+) a232342_list -- Reinhard Zumkeller, Dec 16 2013, Nov 22 2013 CROSSREFS Cf. A077065, A077068, A232359, A232361. Partial sums of A232342. Sequence in context: A085805 A119413 A044446 * A323183 A072977 A341895 Adjacent sequences:  A232218 A232219 A232220 * A232222 A232223 A232224 KEYWORD sign,look AUTHOR N. J. A. Sloane, Nov 22 2013, based on a posting by V.J. Pohjola to the Sequence Fans Mailing List, Nov 22 2013 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.

Last modified December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)