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A231684 a(n) = Sum_{i=0..n} digsum_9(i), where digsum_9(i) = A053830(i). 4
0, 1, 3, 6, 10, 15, 21, 28, 36, 37, 39, 42, 46, 51, 57, 64, 72, 81, 83, 86, 90, 95, 101, 108, 116, 125, 135, 138, 142, 147, 153, 160, 168, 177, 187, 198, 202, 207, 213, 220, 228, 237, 247, 258, 270, 275, 281, 288, 296, 305, 315, 326, 338, 351, 357, 364, 372, 381, 391, 402, 414, 427, 441, 448, 456, 465, 475, 486, 498, 511, 525, 540, 548, 557, 567, 578, 590, 603, 617, 632 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

LINKS

Table of n, a(n) for n=0..79.

Jean Coquet, Power sums of digital sums, J. Number Theory 22 (1986), no. 2, 161-176.

P. J. Grabner, P. Kirschenhofer, H. Prodinger, R. F. Tichy, On the moments of the sum-of-digits function, PDF, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), 263-271, Kluwer Acad. Publ., Dordrecht, 1993.

J.-L. Mauclaire, Leo Murata, On q-additive functions. I, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 6, 274-276.

J.-L. Mauclaire, Leo Murata, On q-additive functions. II, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 9, 441-444.

J. R. Trollope, An explicit expression for binary digital sums, Math. Mag. 41 1968 21-25.

PROG

(PARI) a(n) = sum(i=0, n, sumdigits(i, 9)); \\ Michel Marcus, Sep 20 2017

CROSSREFS

Cf. A053830, A231685, A231686, A231687.

Sequence in context: A033440 A067525 A130487 * A108923 A033441 A107082

Adjacent sequences:  A231681 A231682 A231683 * A231685 A231686 A231687

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Nov 13 2013

STATUS

approved

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Last modified September 17 16:57 EDT 2019. Contains 327136 sequences. (Running on oeis4.)