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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 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 22 12:34 EDT 2020. Contains 337289 sequences. (Running on oeis4.)