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A231502
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a(n) = Sum_{i=0..n} wt(i)^4, where wt() = A000120().
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4
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0, 1, 2, 18, 19, 35, 51, 132, 133, 149, 165, 246, 262, 343, 424, 680, 681, 697, 713, 794, 810, 891, 972, 1228, 1244, 1325, 1406, 1662, 1743, 1999, 2255, 2880, 2881, 2897, 2913, 2994, 3010, 3091, 3172, 3428, 3444, 3525, 3606, 3862, 3943, 4199, 4455, 5080, 5096, 5177, 5258, 5514, 5595, 5851, 6107, 6732, 6813, 7069
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OFFSET
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0,3
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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), Kluwer Acad. Publ., Dordrecht, 1993, pp. 263-271; alternative link.
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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a(n) ~ n * (log(n)/(2*log(2)))^4 + O(n*log(n)^3) (Stolarsky, 1977). - Amiram Eldar, Jan 20 2022
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MATHEMATICA
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Accumulate @ (Table[DigitCount[n, 2, 1], {n, 0, 60}]^4) (* Amiram Eldar, Jan 20 2022 *)
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PROG
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(PARI) a(n) = sum(i=0, n, hammingweight(i)^4); \\ Michel Marcus, Nov 12 2013
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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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