%I #7 Sep 20 2017 11:46:25
%S 0,1,9,36,100,225,441,442,450,477,541,666,882,1225,1233,1260,1324,
%T 1449,1665,2008,2520,2547,2611,2736,2952,3295,3807,4536,4600,4725,
%U 4941,5284,5796,6525,7525,7650,7866,8209,8721,9450,10450,11781,11997,12340,12852,13581,14581,15912,17640,17641,17649,17676,17740,17865,18081,18424,18432,18459,18523,18648,18864,19207
%N a(n) = Sum_{i=0..n} digsum_7(i)^3, where digsum_7(i) = A053828(i).
%H Jean Coquet, <a href="https://doi.org/10.1016/0022-314X(86)90067-3">Power sums of digital sums</a>, J. Number Theory 22 (1986), no. 2, 161-176.
%H P. J. Grabner, P. Kirschenhofer, H. Prodinger, R. F. Tichy, <a href="http://math.sun.ac.za/~hproding/abstract/abs_80.htm">On the moments of the sum-of-digits function</a>, <a href="http://math.sun.ac.za/~hproding/pdffiles/st_andrews.pdf">PDF</a>, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), 263-271, Kluwer Acad. Publ., Dordrecht, 1993.
%H J.-L. Mauclaire, Leo Murata, <a href="https://dx.doi.org/10.3792/pjaa.59.274">On q-additive functions. I</a>, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 6, 274-276.
%H J.-L. Mauclaire, Leo Murata, <a href="https://dx.doi.org/10.3792/pjaa.59.441">On q-additive functions. II</a>, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 9, 441-444.
%H J. R. Trollope, <a href="http://www.jstor.org/stable/2687954">An explicit expression for binary digital sums</a>, Math. Mag. 41 1968 21-25.
%o (PARI) a(n) = sum(i=0, n, sumdigits(i, 7)^3); \\ _Michel Marcus_, Sep 20 2017
%Y Cf. A053828, A231676, A231678, A231679.
%K nonn,base
%O 0,3
%A _N. J. A. Sloane_, Nov 13 2013