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%I #13 Jan 20 2022 07:38:57
%S 0,1,9,10,18,45,53,80,144,145,153,180,188,215,279,306,370,495,503,530,
%T 594,621,685,810,874,999,1215,1216,1224,1251,1259,1286,1350,1377,1441,
%U 1566,1574,1601,1665,1692,1756,1881,1945,2070,2286,2313,2377,2502,2566,2691,2907,3032,3248,3591,3599,3626,3690,3717,3781,3906,3970,4095,4311,4338,4402,4527,4591,4716
%N a(n) = Sum_{i=0..n} digsum_3(i)^3, where digsum_3(i) = A053735(i).
%H Amiram Eldar, <a href="/A231504/b231504.txt">Table of n, a(n) for n = 0..10000</a>
%H Jean Coquet, <a href="https://doi.org/10.1016/0022-314X(86)90067-3">Power sums of digital sums</a>, J. Number Theory, Vol. 22, No. 2 (1986), pp. 161-176.
%H P. J. Grabner, P. Kirschenhofer, H. Prodinger and 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), Kluwer Acad. Publ., Dordrecht, 1993, pp. 263-271.
%H J.-L. Mauclaire and 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., Vol. 59, No. 6 (1983), pp. 274-276.
%H J.-L. Mauclaire and 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., Vol. 59, No. 9 (1983), pp. 441-444.
%H J. R. Trollope, <a href="http://www.jstor.org/stable/2687954">An explicit expression for binary digital sums</a>, Math. Mag., Vol. 41, No. 1 (1968), pp. 21-25.
%t Accumulate @ Array[(Plus @@ IntegerDigits[#, 3])^3 &, 70, 0] (* _Amiram Eldar_, Jan 20 2022 *)
%o (PARI) a(n) = sum(i=0, n, sumdigits(i, 3)^3); \\ _Michel Marcus_, Sep 20 2017
%Y Cf. A053735, A094345, A231503, A231505.
%K nonn,base
%O 0,3
%A _N. J. A. Sloane_, Nov 13 2013
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