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A194102 a(n) = Sum_{j=1..n} floor(j*sqrt(2)); n-th partial sum of Beatty sequence for sqrt(2). 4
1, 3, 7, 12, 19, 27, 36, 47, 59, 73, 88, 104, 122, 141, 162, 184, 208, 233, 259, 287, 316, 347, 379, 412, 447, 483, 521, 560, 601, 643, 686, 731, 777, 825, 874, 924, 976, 1029, 1084, 1140, 1197, 1256, 1316, 1378, 1441, 1506, 1572, 1639, 1708, 1778 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The natural fractal sequence of A194102 is A194103; the natural interspersion is A194104.  See A194029 for definitions.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

MATHEMATICA

c[n_]:=Sum[Floor[j*Sqrt[2]], {j, 1, n}]; Table[c[n], {n, 1, 90}]

PROG

(PARI) for(n=1, 100, print1(sum(k=1, n, floor(k*sqrt(2))), ", ")) \\ G. C. Greubel, Jun 05 2018

(MAGMA) [(&+[Floor(k*Sqrt(2)): k in [1..n]]): n in [1..100]]; // G. C. Greubel, Jun 05 2018

CROSSREFS

Cf. A194029, A194103, A194104, A001951.

Sequence in context: A171835 A324125 A212293 * A006317 A194147 A077043

Adjacent sequences:  A194099 A194100 A194101 * A194103 A194104 A194105

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 15 2011

STATUS

approved

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Last modified July 23 19:33 EDT 2019. Contains 325263 sequences. (Running on oeis4.)