

A097508


Differences between floor(n*sqrt(2)) and n.


4



0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30, 30, 31, 31, 31
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OFFSET

0,6


COMMENTS

a(2*n) = 2*a(n) + A197879(n).  Robert Israel, Aug 21 2014


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000
Heinz H. Bauschke, Minh N. Dao, Scott B. Lindstrom, The DouglasRachford algorithm for a hyperplane and a doubleton, arXiv:1804.08880 [math.OC], 2018.
M. Celaya, F. Ruskey, Morphic Words and Nested Recurrence Relations, arXiv preprint arXiv:1307.0153 [math.CO], 2013.


FORMULA

a(n) = (floor(n / cos(45 degrees)))  n.
a(n) = A001951(n)n.  R. J. Mathar, Sep 19 2010
a(n) = floor((sqrt(2)1)*n). [CelayaRuskey].  N. J. A. Sloane, Nov 14 2013


MAPLE

seq(floor(n*sqrt(2))  n, n = 0 .. 100); # Robert Israel, Aug 21 2014


MATHEMATICA

Table[Floor[n Sqrt[2]]n, {n, 0, 80}] (* Harvey P. Dale, Dec 04 2014 *)


PROG

(PARI) a(n)=sqrtint(2*n^2)n \\ Charles R Greathouse IV, Sep 02 2015
(MAGMA) [Floor(n*Sqrt(2))  n: n in [0..100]]; // G. C. Greubel, Mar 27 2018


CROSSREFS

Cf. A001951, A197879.
Sequence in context: A172476 A172267 A231151 * A244225 A109964 A247366
Adjacent sequences: A097505 A097506 A097507 * A097509 A097510 A097511


KEYWORD

easy,nonn


AUTHOR

Odimar Fabeny, Aug 26 2004


EXTENSIONS

Extended by R. J. Mathar, Sep 19 2010
Definition edited by Robert Israel, Aug 21 2014


STATUS

approved



