OFFSET
0,3
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..10000
Jean Coquet, Power sums of digital sums, J. Number Theory, Vol. 22, No. 2 (1986), pp. 161-176.
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.
J.-L. Mauclaire and Leo Murata, On q-additive functions. II, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 9 (1983), pp. 441-444.
Kennth B. Stolarsky, Power and exponential sums of digital sums related to binomial coefficient parity, SIAM J. Appl. Math., Vol. 32, No. 4 (1977), pp. 717-730.
J. R. Trollope, An explicit expression for binary digital sums, Math. Mag., Vol. 41, No. 1 (1968), pp. 21-25.
FORMULA
a(n) ~ n * (log(n)/(2*log(2)))^4 + O(n*log(n)^3) (Stolarsky, 1977). - Amiram Eldar, Jan 20 2022
a(n) = Sum_{k=0..floor(log_2(n+1))} k^4 * A360189(n,k). - Alois P. Heinz, Mar 06 2023
MATHEMATICA
Accumulate @ (Table[DigitCount[n, 2, 1], {n, 0, 60}]^4) (* Amiram Eldar, Jan 20 2022 *)
PROG
(PARI) a(n) = sum(i=0, n, hammingweight(i)^4); \\ Michel Marcus, Nov 12 2013
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Nov 12 2013
STATUS
approved