A231666 a(n) = Sum_{i=0..n} digsum_4(i)^3, where digsum_4(i) = A053737(i).

0, 1, 9, 36, 37, 45, 72, 136, 144, 171, 235, 360, 387, 451, 576, 792, 793, 801, 828, 892, 900, 927, 991, 1116, 1143, 1207, 1332, 1548, 1612, 1737, 1953, 2296, 2304, 2331, 2395, 2520, 2547, 2611, 2736, 2952, 3016, 3141, 3357, 3700, 3825, 4041, 4384, 4896, 4923, 4987, 5112, 5328, 5392, 5517, 5733, 6076, 6201, 6417, 6760, 7272, 7488, 7831, 8343, 9072, 9073, 9081, 9108, 9172

Offset

0,3

Links

Marius A. Burtea, 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.

Prog

(PARI) a(n) = sum(i=0, n, sumdigits(i, 4)^3); \\ Michel Marcus, Sep 20 2017
(MATLAB) for u=0:2000; v(u+1)=sum(dec2base(u, 4)-'0'); end
sol=cumsum(v.^3); % Marius A. Burtea, Jan 18 2019

Crossrefs

Cf. A053737, A231664, A231665, A231667.

Sequence in context: A267081 A020297 A330907 * A143224 A192610 A319958

Adjacent sequences: A231663 A231664 A231665 * A231667 A231668 A231669

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved