

A194235


a(n) = [Sum_{k=1..n} (k/8)], where [ ]=floor, ( )=fractional part.


3



0, 0, 0, 1, 1, 2, 3, 3, 3, 3, 4, 4, 5, 6, 7, 7, 7, 7, 7, 8, 8, 9, 10, 10, 10, 10, 11, 11, 12, 13, 14, 14, 14, 14, 14, 15, 15, 16, 17, 17, 17, 17, 18, 18, 19, 20, 21, 21, 21, 21, 21, 22, 22, 23, 24, 24, 24, 24, 25, 25, 26, 27, 28, 28, 28, 28, 28, 29, 29, 30, 31, 31, 31, 31
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OFFSET

1,6


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000


FORMULA

From Chai Wah Wu, Jun 10 2020: (Start)
a(n) = a(n1) + a(n16)  a(n17) for n > 17.
G.f.: x*(x^14 + x^13 + x^12 + x^10 + x^6 + x^5 + x^3)/(x^17  x^16  x + 1). (End)


MATHEMATICA

r = 1/8;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}] (* A194235 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194236 *)


PROG

(PARI) a(n) = floor(sum(k=1, n, frac(k/8))); \\ Michel Marcus, Nov 03 2017


CROSSREFS

Cf. A194236.
Sequence in context: A189627 A194227 A194819 * A029120 A078428 A337634
Adjacent sequences: A194232 A194233 A194234 * A194236 A194237 A194238


KEYWORD

nonn


AUTHOR

Clark Kimberling, Aug 20 2011


STATUS

approved



