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A231685 a(n) = Sum_{i=0..n} digsum_9(i)^2, where digsum_9(i) = A053830(i). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

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

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

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

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

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

LINKS

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

MATHEMATICA

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

CROSSREFS

Cf. A053830, A231684-A231687.

Sequence in context: A096893 A231677 A231681 * A074784 A109678 A000330

Adjacent sequences:  A231682 A231683 A231684 * A231686 A231687 A231688

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Nov 13 2013

STATUS

approved

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Last modified July 21 04:27 EDT 2017. Contains 289632 sequences.