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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
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
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
Partial sums of A232342.
Sequence in context: A085805 A119413 A044446 * A323183 A072977 A341895
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