A231685 a(n) = Sum_{i=0..n} digsum_9(i)^2, where digsum_9(i) = A053830(i).

0, 1, 5, 14, 30, 55, 91, 140, 204, 205, 209, 218, 234, 259, 295, 344, 408, 489, 493, 502, 518, 543, 579, 628, 692, 773, 873, 882, 898, 923, 959, 1008, 1072, 1153, 1253, 1374, 1390, 1415, 1451, 1500, 1564, 1645, 1745, 1866, 2010, 2035, 2071, 2120, 2184, 2265, 2365, 2486, 2630, 2799, 2835, 2884, 2948, 3029, 3129, 3250, 3394, 3563, 3759, 3808, 3872, 3953, 4053, 4174, 4318

Offset: 0

Author

N. J. A. Sloane, Nov 13 2013

Keywords

• nonn
• base

Comments

Partial sums of ((the total of the digits of i in base 9) squared). - Harvey P. Dale, Nov 26 2013

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• 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.

Crossrefs

Cf. A053830, A231684, A231686, A231687.

Programs

Mathematica

Accumulate[Table[Total[IntegerDigits[n,9]]^2,{n,0,100}]] (* Harvey P. Dale, Nov 26 2013 *)

PARI

a(n) = sum(i=0, n, sumdigits(i, 9)^2); \\ Michel Marcus, Sep 20 2017