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A231664 a(n) = Sum_{i=0..n} digsum_4(i), where digsum_4(i) = A053737(i). 5
0, 1, 3, 6, 7, 9, 12, 16, 18, 21, 25, 30, 33, 37, 42, 48, 49, 51, 54, 58, 60, 63, 67, 72, 75, 79, 84, 90, 94, 99, 105, 112, 114, 117, 121, 126, 129, 133, 138, 144, 148, 153, 159, 166, 171, 177, 184, 192, 195, 199, 204, 210, 214, 219, 225, 232, 237, 243, 250, 258, 264, 271, 279, 288, 289, 291, 294, 298, 300, 303, 307, 312, 315, 319, 324, 330, 334, 339, 345, 352, 354, 357 (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

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

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.

FORMULA

G.f. g(x) satisfies g(x) = (1+x+x^2+x^3)^2*g(x^4) + (x+2*x^2+3*x^3)/(1-x-x^4+x^5). - Robert Israel, Sep 20 2017

MAPLE

ListTools:-PartialSums([seq(convert(convert(n, base, 4), `+`), n=0..200)]); # Robert Israel, Sep 20 2017

PROG

(PARI) a(n) = sum(i=0, n, sumdigits(i, 4)); \\ Michel Marcus, Sep 20 2017

CROSSREFS

Cf. A053737, A231665, A231666, A231667.

Sequence in context: A297249 A061641 A085359 * A087916 A296693 A282585

Adjacent sequences:  A231661 A231662 A231663 * A231665 A231666 A231667

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Nov 13 2013

STATUS

approved

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Last modified October 15 15:39 EDT 2018. Contains 316236 sequences. (Running on oeis4.)