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Number of points with integer coordinates inside the equilateral triangle with base [0,n].
1

%I #20 Jul 07 2023 14:45:49

%S 1,2,4,6,10,14,20,26,33,40,49,58,69,80,93,106,120,134,150,166,184,202,

%T 222,242,263,284,307,330,355,380,406,432,460,488,518,548,580,612,645,

%U 678,713,748,785,822,861,900,940,980,1022

%N Number of points with integer coordinates inside the equilateral triangle with base [0,n].

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

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

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

%o (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

%K nonn

%O 0,2

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

%E Offset set to 0 and a(0) prepended by _Michel Marcus_, Aug 05 2013