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%I #9 Dec 22 2020 13:59:54
%S 0,1,9,36,100,225,441,784,1296,1297,1305,1332,1396,1521,1737,2080,
%T 2592,3321,3329,3356,3420,3545,3761,4104,4616,5345,6345,6372,6436,
%U 6561,6777,7120,7632,8361,9361,10692,10756,10881,11097,11440,11952,12681,13681,15012,16740,16865,17081,17424,17936,18665,19665,20996,22724,24921,25137,25480,25992,26721,27721,29052
%N a(n) = Sum_{i=0..n} digsum_9(i)^3, where digsum_9(i) = A053830(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.
%t Accumulate[Table[Total[IntegerDigits[n,9]]^3,{n,0,60}]] (* _Harvey P. Dale_, Dec 22 2020 *)
%o (PARI) a(n) = sum(i=0, n, sumdigits(i, 9)^3); \\ _Michel Marcus_, Sep 20 2017
%Y Cf. A053830, A231684, A231685, A231687.
%K nonn,base
%O 0,3
%A _N. J. A. Sloane_, Nov 13 2013
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