A194236 Partial sums of A194235.

0, 0, 0, 1, 2, 4, 7, 10, 13, 16, 20, 24, 29, 35, 42, 49, 56, 63, 70, 78, 86, 95, 105, 115, 125, 135, 146, 157, 169, 182, 196, 210, 224, 238, 252, 267, 282, 298, 315, 332, 349, 366, 384, 402, 421, 441, 462, 483, 504, 525, 546, 568, 590, 613, 637, 661, 685

Offset

1,5

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-16) - 2*a(n-17) + a(n-18) for n > 18.

G.f.: x*(-x^14 - x^13 - x^12 - x^10 - x^6 - x^5 - x^3)/(x^18 - 2*x^17 + x^16 - x^2 + 2*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) f(n) = floor(sum(k=1, n, frac(k/8)));
a(n) = sum(k=1, n, f(k)); \\ Michel Marcus, Nov 03 2017

Crossrefs

Cf. A194235.

Sequence in context: A001195 A295513 A194228 * A127762 A137281 A287420

Adjacent sequences: A194233 A194234 A194235 * A194237 A194238 A194239

Keyword

nonn

Author

Clark Kimberling, Aug 20 2011

Status

approved