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[sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=1/2+sqrt(8).
2

%I #5 Mar 30 2012 18:57:40

%S 0,0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,11,11,11,12,13,13,14,14,15,16,16,

%T 16,17,17,18,19,19,19,20,20,21,22,22,22,23,23,24,24,25,25,26,26,26,27,

%U 27,27,28,28,29,29,29,30,31,31,31,32,32,32,33,33,33,34,35,35,36

%N [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=1/2+sqrt(8).

%t r = 1/2+Sqrt[8];

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

%t Table[a[n], {n, 1, 90}] (* A194179 *)

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

%t Table[s[n], {n, 1, 100}] (* A194180 *)

%Y Cf. A194180.

%K nonn

%O 1,4

%A _Clark Kimberling_, Aug 18 2011