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A231664
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a(n) = Sum_{i=0..n} digsum_4(i), where digsum_4(i) = A053737(i).
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6
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0, 1, 3, 6, 7, 9, 12, 16, 18, 21, 25, 30, 33, 37, 42, 48, 49, 51, 54, 58, 60, 63, 67, 72, 75, 79, 84, 90, 94, 99, 105, 112, 114, 117, 121, 126, 129, 133, 138, 144, 148, 153, 159, 166, 171, 177, 184, 192, 195, 199, 204, 210, 214, 219, 225, 232, 237, 243, 250, 258, 264, 271, 279, 288, 289, 291, 294, 298, 300, 303, 307, 312, 315, 319, 324, 330, 334, 339, 345, 352, 354, 357
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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Jean-Paul Allouche and Jeffrey Shallit, Automatic sequences, Cambridge University Press, 2003, p. 94.
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LINKS
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P. J. Grabner, P. Kirschenhofer, H. Prodinger and R. F. Tichy, On the moments of the sum-of-digits function, PDF, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), pp. 263-271, Kluwer Acad. Publ., Dordrecht, 1993.
J.-L. Mauclaire and Leo Murata, On q-additive functions. I, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 6 (1983), pp. 274-276.
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FORMULA
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G.f.: g(x) satisfies g(x) = (1+x+x^2+x^3)^2*g(x^4) + (x+2*x^2+3*x^3)/(1-x-x^4+x^5). - Robert Israel, Sep 20 2017
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MAPLE
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ListTools:-PartialSums([seq(convert(convert(n, base, 4), `+`), n=0..200)]); # Robert Israel, Sep 20 2017
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MATHEMATICA
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Table[Sum[Total[IntegerDigits[j, 4]], {j, 0, n}], {n, 0, 100}] (* G. C. Greubel, Feb 16 2019 *)
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PROG
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(PARI) a(n) = sum(i=0, n, sumdigits(i, 4)); \\ Michel Marcus, Sep 20 2017
(Magma) [(&+[&+Intseq(j, 4): j in [0..n]]): n in [0..100]]; // G. C. Greubel, Feb 16 2019
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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