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A231500 a(n) = Sum_{i=0..n} wt(i)^2, where wt(i) = A000120(i). 3
0, 1, 2, 6, 7, 11, 15, 24, 25, 29, 33, 42, 46, 55, 64, 80, 81, 85, 89, 98, 102, 111, 120, 136, 140, 149, 158, 174, 183, 199, 215, 240, 241, 245, 249, 258, 262, 271, 280, 296, 300, 309, 318, 334, 343, 359, 375, 400, 404, 413, 422, 438, 447, 463, 479, 504, 513, 529, 545, 570, 586, 611, 636, 672, 673, 677, 681, 690, 694 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Stolarsky (1977) has an extensive bibliography.

LINKS

Ivan Neretin, Table of n, a(n) for n = 0..1024

Jean Coquet, Power sums of digital sums, J. Number Theory 22 (1986), no. 2, 161-176.

P. J. Grabner, P. Kirschenhofer, H. Prodinger, R. F. Tichy, On the moments of the sum-of-digits function, PDF, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), 263-271, Kluwer Acad. Publ., Dordrecht, 1993.

J.-L. Mauclaire, Leo Murata, On q-additive functions. I, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 6, 274-276.

J.-L. Mauclaire, Leo Murata, On q-additive functions. II, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 9, 441-444.

K. B. Stolarsky, Power and exponential sums of digital sums related to binomial coefficient parity, SIAM J. Appl. Math., 32 (1977), 717-730.

J. R. Trollope, An explicit expression for binary digital sums, Math. Mag. 41 1968 21-25.

FORMULA

Stolarsky (1977) studies the asymptotics.

MAPLE

digsum:=proc(n, B) local a; a := convert(n, base, B):

add(a[i], i=1..nops(a)): end;

f:=proc(n, k, B) global digsum; local i;

add( digsum(i, B)^k, i=0..n); end;

[seq(f(n, 1, 2), n=0..100)]; #A000788

[seq(f(n, 2, 2), n=0..100)]; #A231500

[seq(f(n, 3, 2), n=0..100)]; #A231501

[seq(f(n, 4, 2), n=0..100)]; #A231502

MATHEMATICA

FoldList[#1 + DigitCount[#2, 2, 1]^2 &, 0, Range[1, 68]] (* Ivan Neretin, May 21 2015 *)

PROG

(PARI) a(n) = sum(i=0, n, hammingweight(i)^2); \\ Michel Marcus, Sep 20 2017

CROSSREFS

Cf. A000120, A000788, A231501, A231502.

Sequence in context: A214991 A286995 A088227 * A174000 A241720 A224082

Adjacent sequences:  A231497 A231498 A231499 * A231501 A231502 A231503

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Nov 12 2013

STATUS

approved

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Last modified February 24 22:04 EST 2020. Contains 332216 sequences. (Running on oeis4.)