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

Author

Clark Kimberling, Aug 20 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1).

Crossrefs

Cf. A194237.

Programs

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 *)

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)