A194224 Partial sums of A194223.

0, 0, 1, 2, 4, 6, 8, 11, 14, 18, 23, 28, 33, 38, 44, 50, 57, 64, 71, 79, 87, 96, 106, 116, 126, 136, 147, 158, 170, 182, 194, 207, 220, 234, 249, 264, 279, 294, 310, 326, 343, 360, 377, 395, 413, 432, 452, 472, 492, 512, 533, 554, 576, 598, 620, 643, 666

Offset

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

From Chai Wah Wu, Jun 10 2020: (Start)

a(n) = 2*a(n-1) - a(n-2) + a(n-12) - 2*a(n-13) + a(n-14) for n > 14.

G.f.: x*(-x^10 - x^9 - x^7 - x^4 - x^2)/(x^14 - 2*x^13 + x^12 - x^2 + 2*x - 1). (End)

Mathematica

r = 1/6;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194223 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194224 *)

Prog

(PARI) for(n=1, 50, print1(sum(j=1, n, floor(sum(k=1, j, frac(k/6)))), ", ")) \\ G. C. Greubel, Oct 29 2017

Crossrefs

Cf. A194223.

Sequence in context: A194162 A084627 A321531 * A194252 A205727 A213609

Adjacent sequences: A194221 A194222 A194223 * A194225 A194226 A194227

Keyword

nonn

Author

Clark Kimberling, Aug 19 2011

Status

approved