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A231667 a(n) = Sum_{i=0..n} digsum_4(i)^4, where digsum_4(i) = A053737(i).

%I A231667 #12 Jan 18 2019 09:12:31
%S A231667 0,1,17,98,99,115,196,452,468,549,805,1430,1511,1767,2392,3688,3689,
%T A231667 3705,3786,4042,4058,4139,4395,5020,5101,5357,5982,7278,7534,8159,
%U A231667 9455,11856,11872,11953,12209,12834,12915,13171,13796,15092,15348,15973,17269,19670,20295,21591,23992,28088,28169,28425,29050,30346,30602,31227,32523,34924,35549,36845,39246,43342
%N A231667 a(n) = Sum_{i=0..n} digsum_4(i)^4, where digsum_4(i) = A053737(i).
%H A231667 Marius A. Burtea, <a href="/A231667/b231667.txt">Table of n, a(n) for n = 0..10000</a>
%H A231667 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 A231667 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 A231667 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 A231667 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 A231667 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.
%o A231667 (PARI) a(n) = sum(i=0, n, sumdigits(i, 4)^4); \\ _Michel Marcus_, Sep 20 2017
%Y A231667 Cf. A053737, A231664, A231665, A231666.
%K A231667 nonn,base
%O A231667 0,3
%A A231667 _N. J. A. Sloane_, Nov 13 2013