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A194220
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[sum{(k/4) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.
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3
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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)
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OFFSET
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1,6
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..5000
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FORMULA
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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)
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A194221.
Sequence in context: A155934 A251719 A130822 * A189627 A194227 A194819
Adjacent sequences: A194217 A194218 A194219 * A194221 A194222 A194223
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Aug 19 2011
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STATUS
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approved
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