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A194162
Partial sums of A194161.
3
0, 1, 2, 4, 6, 8, 11, 14, 18, 22, 27, 33, 39, 46, 53, 61, 69, 77, 86, 95, 105, 115, 126, 138, 150, 163, 176, 190, 204, 218, 233, 248, 264, 280, 296, 313, 331, 349, 368, 387, 407, 428, 449, 471, 493, 515, 538, 562, 586, 611, 636, 661, 687, 714, 741, 769
OFFSET
1,3
LINKS
MATHEMATICA
r = Sqrt[2];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]
s[n_] := Sum[a[k], {k, 1, n}] (* A194161 *)
Table[s[n], {n, 1, 100}]
b[n_] := Floor[n (n + 1) r/2] - Sum[Floor[k*r], {k, 1, n}]
Table[b[n], {n, 1, 90}] (* A194162 *)
PROG
(PARI) b(n) = floor(sum(k=1, n, frac(k*sqrt(2))));
a(n) = sum(k=1, n, b(k)); \\ Michel Marcus, Nov 06 2017
CROSSREFS
Cf. A194161.
Sequence in context: A032514 A011858 A183144 * A084627 A321531 A194224
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 18 2011
STATUS
approved