A231665 a(n) = Sum_{i=0..n} digsum_4(i)^2, where digsum_4(i) = A053737(i).

0, 1, 5, 14, 15, 19, 28, 44, 48, 57, 73, 98, 107, 123, 148, 184, 185, 189, 198, 214, 218, 227, 243, 268, 277, 293, 318, 354, 370, 395, 431, 480, 484, 493, 509, 534, 543, 559, 584, 620, 636, 661, 697, 746, 771, 807, 856, 920, 929, 945, 970, 1006, 1022, 1047, 1083, 1132, 1157, 1193, 1242, 1306, 1342, 1391, 1455, 1536, 1537, 1541, 1550, 1566, 1570, 1579, 1595, 1620, 1629

Offset

0,3

Links

Marius A. Burtea, Table of n, a(n) for n = 0..10000

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.

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

Prog

(PARI) a(n) = sum(i=0, n, sumdigits(i, 4)^2); \\ Michel Marcus, Sep 20 2017
(MATLAB) for u=0:2000; v(u+1)=sum(dec2base(u, 4)-'0'); end
sol=cumsum(v.^2); % Marius A. Burtea, Jan 18 2019

Crossrefs

Cf. A053737, A231664, A231666, A231667.

Sequence in context: A168213 A175485 A174657 * A160709 A067113 A101774

Adjacent sequences: A231662 A231663 A231664 * A231666 A231667 A231668

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved