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A194165 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r = (1+sqrt(5))/2, the golden ratio. 3
0, 0, 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 9, 9, 10, 11, 11, 12, 12, 12, 13, 13, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 20, 21, 21, 21, 22, 23, 23, 23, 24, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 33, 34, 34, 35, 36, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
MATHEMATICA
r = GoldenRatio;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}] (* A194165 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194166 *)
PROG
(PARI) a(n) = floor(sum(k=1, n, frac((1+sqrt(5))*k/2))); \\ Michel Marcus, Nov 12 2017
CROSSREFS
Cf. A194166.
Sequence in context: A113512 A338624 A194169 * A004524 A265409 A126257
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 18 2011
STATUS
approved

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)