|
%I #16 Oct 06 2018 03:55:31
%S 0,1,5,14,30,55,91,140,204,205,209,218,234,259,295,344,408,489,493,
%T 502,518,543,579,628,692,773,873,882,898,923,959,1008,1072,1153,1253,
%U 1374,1390,1415,1451,1500,1564,1645,1745,1866,2010,2035,2071,2120,2184,2265,2365,2486,2630,2799,2835,2884,2948,3029,3129,3250,3394,3563,3759,3808,3872,3953,4053,4174,4318
%N a(n) = Sum_{i=0..n} digsum_9(i)^2, where digsum_9(i) = A053830(i).
%C Partial sums of ((the total of the digits of i in base 9) squared). - _Harvey P. Dale_, Nov 26 2013
%H Harvey P. Dale, <a href="/A231685/b231685.txt">Table of n, a(n) for n = 0..1000</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 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]]^2,{n,0,100}]] (* _Harvey P. Dale_, Nov 26 2013 *)
%o (PARI) a(n) = sum(i=0, n, sumdigits(i, 9)^2); \\ _Michel Marcus_, Sep 20 2017
%Y Cf. A053830, A231684, A231686, A231687.
%K nonn,base
%O 0,3
%A _N. J. A. Sloane_, Nov 13 2013
|
