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A194220 [sum{(k/4) : 1<=k<=n}], where [ ]=floor, ( )=fractional part. 3
0, 0, 1, 1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 6, 7, 7, 7, 8, 9, 9, 9, 9, 10, 10, 10, 11, 12, 12, 12, 12, 13, 13, 13, 14, 15, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 18, 19, 19, 19, 20, 21, 21, 21, 21, 22, 22, 22, 23, 24, 24, 24, 24, 25, 25, 25, 26, 27, 27, 27, 27, 28 (list; graph; refs; listen; history; text; internal format)
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(n-1) + a(n-8) - a(n-9) for n > 9.

G.f.: x*(x^6 + x^5 + x^2)/(x^9 - x^8 - x + 1). (End)

MATHEMATICA

r = 1/4;

a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]

Table[a[n], {n, 1, 90}]    (* A194220 *)

s[n_] := Sum[a[k], {k, 1, n}]

Table[s[n], {n, 1, 100}]   (* A194221 *)

CROSSREFS

Cf. A194221.

Sequence in context: A155934 A251719 A130822 * A189627 A194227 A194819

Adjacent sequences:  A194217 A194218 A194219 * A194221 A194222 A194223

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 19 2011

STATUS

approved

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Last modified October 3 16:41 EDT 2022. Contains 357237 sequences. (Running on oeis4.)