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%I #17 Mar 06 2023 18:12:47
%S 0,1,2,10,11,19,27,54,55,63,71,98,106,133,160,224,225,233,241,268,276,
%T 303,330,394,402,429,456,520,547,611,675,800,801,809,817,844,852,879,
%U 906,970,978,1005,1032,1096,1123,1187,1251,1376,1384,1411,1438,1502,1529,1593,1657,1782,1809,1873,1937,2062,2126,2251
%N a(n) = Sum_{i=0..n} wt(i)^3, where wt() = A000120().
%H Amiram Eldar, <a href="/A231501/b231501.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; <a href="https://math.sun.ac.za/prodinger/pdffiles/st_andrews.pdf">alternative link</a>.
%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 Kenneth B. Stolarsky, <a href="http://dx.doi.org/10.1137/0132060">Power and exponential sums of digital sums related to binomial coefficient parity</a>, SIAM J. Appl. Math., Vol. 32, No. 4 (1977), pp. 717-730.
%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.
%F a(n) ~ n * (log(n)/(2*log(2)))^3 + O(n*log(n)^2) (Stolarsky, 1977). - _Amiram Eldar_, Jan 20 2022
%F a(n) = Sum_{k=0..floor(log_2(n+1))} k^3 * A360189(n,k). - _Alois P. Heinz_, Mar 06 2023
%t Accumulate @ (Table[DigitCount[n, 2, 1], {n, 0, 60}]^3) (* _Amiram Eldar_, Jan 20 2022 *)
%o (PARI) a(n) = sum(i=0, n, hammingweight(i)^3); \\ _Michel Marcus_, Sep 20 2017
%Y Cf. A000120, A000788, A231500, A231502, A360189.
%K nonn,base
%O 0,3
%A _N. J. A. Sloane_, Nov 12 2013
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