A194221 - OEIS

%I #13 Jun 10 2020 22:45:38

%S 0,0,1,2,3,5,8,11,14,17,21,25,29,34,40,46,52,58,65,72,79,87,96,105,

%T 114,123,133,143,153,164,176,188,200,212,225,238,251,265,280,295,310,

%U 325,341,357,373,390,408,426,444,462,481,500,519,539,560,581,602

%N Partial sums of A194220.

%H G. C. Greubel, <a href="/A194221/b194221.txt">Table of n, a(n) for n = 1..1000</a>

%F From _Chai Wah Wu_, Jun 10 2020: (Start)

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

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

%p 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

%t r = 1/4;

%t a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]

%t Table[a[n], {n, 1, 90}]    (* A194220 *)

%t s[n_] := Sum[a[k], {k, 1, n}]

%t Table[s[n], {n, 1, 100}]   (* A194221 *)

%Y Cf. A194220.

%K nonn

%O 1,4

%A _Clark Kimberling_, Aug 19 2011