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A115065 Number of points with integer coordinates inside the equilateral triangle with base [0,n]. 1
1, 2, 4, 6, 10, 14, 20, 26, 33, 40, 49, 58, 69, 80, 93, 106, 120, 134, 150, 166, 184, 202, 222, 242, 263, 284, 307, 330, 355, 380, 406, 432, 460, 488, 518, 548, 580, 612, 645, 678, 713, 748, 785, 822, 861, 900, 940, 980, 1022 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

If one replaces the equilateral triangle by a rectangle isoscele triangle with hypotenuse [0,n], one gets A087811. - Michel Marcus, Aug 05 2013

REFERENCES

Mohammad K. Azarian, A Trigonometric Characterization of  Equilateral Triangle, Problem 336, Mathematics and Computer Education, Vol. 31, No. 1, Winter 1997, p. 96.  Solution published in Vol. 32, No. 1, Winter 1998, pp. 84-85.

Mohammad K. Azarian, Equating Distances and Altitude in an Equilateral Triangle, Problem 316, Mathematics and Computer Education, Vol. 28, No. 3, Fall 1994, p. 337.  Solution published in Vol. 29, No. 3, Fall 1995, pp. 324-325.

LINKS

Table of n, a(n) for n=0..48.

EXAMPLE

For n=0, the triangle is degenerate and there is 1 point (0,0).

For n=1, there are 2 points (0,0) and (0,1).

PROG

(PARI) a(n) = {nb = 0; for (x=0, n, for (y=0, n, if ((x < n/2) && (y <= x*sqrt(3)), nb++); if ((x >= n/2) && (y + x*sqrt(3)) <= n*sqrt(3), nb++); ); ); nb; } \\ Michel Marcus, Aug 05 2013

CROSSREFS

Sequence in context: A277085 A094589 A071425 * A333574 A008804 A001307

Adjacent sequences:  A115062 A115063 A115064 * A115066 A115067 A115068

KEYWORD

nonn

AUTHOR

Neven Juric (neven.juric(AT)apis-it.hr), Jun 20 2006

EXTENSIONS

Offset set to 0 and a(0) prepended by Michel Marcus, Aug 05 2013

STATUS

approved

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)