A194221 Partial sums of A194220.

0, 0, 1, 2, 3, 5, 8, 11, 14, 17, 21, 25, 29, 34, 40, 46, 52, 58, 65, 72, 79, 87, 96, 105, 114, 123, 133, 143, 153, 164, 176, 188, 200, 212, 225, 238, 251, 265, 280, 295, 310, 325, 341, 357, 373, 390, 408, 426, 444, 462, 481, 500, 519, 539, 560, 581, 602

Offset

1,4

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, 1, -2, 1).

Formula

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

a(n) = 2*a(n-1) - a(n-2) + a(n-8) - 2*a(n-9) + a(n-10) for n > 10.

G.f.: x^3*(1 + x^3 + x^4)/((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x^4)). (End)

Maple

seq(coeff(series( x^3*(1+x^3+x^4)/((1-x)^2*(1-x^8)) , x, n+1), x, n), n = 1..60); # G. C. Greubel, Jun 10 2020

Mathematica

r = 1/4;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194220 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194221 *)

Crossrefs

Cf. A194220.

Sequence in context: A078444 A332071 A225087 * A054925 A194248 A375981

Adjacent sequences: A194218 A194219 A194220 * A194222 A194223 A194224

Keyword

nonn

Author

Clark Kimberling, Aug 19 2011

Status

approved