A194238 Partial sums of A194237.

0, 1, 2, 3, 5, 7, 10, 13, 16, 20, 24, 29, 35, 41, 48, 55, 62, 70, 78, 86, 95, 104, 114, 124, 134, 145, 156, 168, 181, 194, 208, 222, 236, 251, 266, 281, 297, 313, 330, 347, 364, 382, 400, 419, 439, 459, 480, 501, 522, 544, 566, 588, 611, 634, 658, 682, 706

Offset

1,3

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^12 - x^11 - x^9 - x^6 - x^4 - x)/(x^18 - 2*x^17 + x^16 - x^2 + 2*x - 1). (End)

Mathematica

r = 3/8;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194237 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194238 *)

Crossrefs

Cf. A194237.

Sequence in context: A008738 A022790 A248360 * A364090 A270192 A053034

Adjacent sequences: A194235 A194236 A194237 * A194239 A194240 A194241

Keyword

nonn

Author

Clark Kimberling, Aug 20 2011

Status

approved