%I #16 Jun 24 2022 23:37:55
%S 0,1,9,36,100,225,441,784,1296,2025,2026,2034,2061,2125,2250,2466,
%T 2809,3321,4050,5050,5058,5085,5149,5274,5490,5833,6345,7074,8074,
%U 9405,9432,9496,9621,9837,10180,10692,11421,12421,13752,15480,15544,15669,15885,16228,16740,17469,18469,19800,21528,23725,23850,24066,24409,24921,25650,26650,27981,29709,31906,34650
%N a(n) = Sum_{i=0..n} digsum(i)^3, where digsum(i) = A007953(i).
%D Grabner, P. J.; Kirschenhofer, P.; Prodinger, H.; Tichy, R. F.; On the moments of the sum-of-digits function. Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), 263-271, Kluwer Acad. Publ., Dordrecht, 1993.
%H Indranil Ghosh, <a href="/A231688/b231688.txt">Table of n, a(n) for n = 0..10000</a>
%H J. Coquet, <a href="http://dx.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 R. E. Kennedy and C. N. Cooper, <a href="http://www.fq.math.ca/Scanned/29-2/kennedy.pdf">An extension of a theorem by Cheo and Yien concerning digital sums</a>, Fibonacci Q. 29, No. 2, 145-149 (1991).
%H J.-L. Mauclaire and Leo Murata, <a href="http://dx.doi.org/10.3792/pjaa.59.274">On q-additive functions</a>, I. Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 6, 274-276.
%H J.-L. Mauclaire and Leo Murata, <a href="http://dx.doi.org/10.3792/pjaa.59.441">On q-additive functions</a>, II. Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 9, 441-444.
%H H. Riede, <a href="http://www.fq.math.ca/Scanned/36-1/riede.pdf">Asymptotic estimation of a sum of digits</a>, Fibonacci Q. 36, No. 1, 72-75 (1998).
%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.
%p See A037123.
%t Accumulate[Table[Total[IntegerDigits[n]]^3,{n,0,60}]] (* _Harvey P. Dale_, Aug 06 2021 *)
%o (PARI) a(n) = sum(i=0, n, sumdigits(i)^3); \\ _Michel Marcus_, Jan 07 2017
%Y Cf. A007953, A037123, A074784, A231689.
%Y Partial sums of A118880.
%K nonn,base
%O 0,3
%A _N. J. A. Sloane_, Nov 13 2013