A232221 a(n) = Sum_{i=1..n} (A077068(i) - A077065(i)).

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

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

Keywords

• sign
• look

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.)

Crossrefs

Cf. A077065, A077068, A232359, A232361.

Partial sums of A232342.

Programs

Haskell

a232221 n = a232221_list !! (n-1)
a232221_list = scanl1 (+) a232342_list
-- Reinhard Zumkeller, Dec 16 2013, Nov 22 2013