A301384 Number of integer-sided triangles of area A188158(n).

1, 2, 2, 1, 2, 1, 2, 1, 4, 1, 1, 4, 2, 2, 2, 1, 4, 3, 1, 2, 1, 2, 4, 2, 2, 1, 1, 6, 3, 1, 5, 3, 3, 2, 2, 1, 4, 1, 2, 4, 8, 5, 1, 2, 1, 3, 1, 15, 2, 4, 2, 1, 5, 1, 6, 2, 1, 3, 4, 3, 1, 2, 2, 1, 2, 4, 5, 1, 5, 4, 1, 2, 3, 5, 1, 1, 1, 6, 2, 4, 2, 1, 2, 1, 17, 4, 1

Offset

1,2

Comments

Nonzero terms of A051584.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Triangle

Example

a(9) = 4 because A188158(9) = 60 corresponding to 4 triangles (a, b, c) = (6, 25, 29), (8, 15, 17), (10, 13, 13) and (13, 13, 24) of area 60.

Maple

A301384 := proc(A::integer)
    local Asqr, s, a, b, c, sol ;
    sol := 0 ;
    Asqr := A^2 ;
    for s in numtheory[divisors](Asqr) do
        if s^2> A then
        for a from 1 to s-1 do
            if modp(Asqr, s-a) = 0 then
                for b from a to s-1 do
                    c := 2*s-a-b ;
                    if s*(s-a)*(s-b)*(s-c) = Asqr and c >= b then
                        sol := sol+1 ;
                    end if;
                end do:
            end if;
        end do:
        end if;
    end do:
    sol ;
end proc:
for n from 3 to 600 do
    a301384 := A301384(n) ;
    if a301384 > 0 then
        printf("%d, \n", a301384) ;
    end if;
end do: # R. J. Mathar, May 02 2018

Mathematica

nn=1000; lst={}; lst2={}; Do[s=(a+b+c)/2; If[IntegerQ[s], area2=s(s-a)(s-b)(s-c); If[0<area2<=nn^2&&IntegerQ[Sqrt[area2]], AppendTo[lst, Sqrt[area2]]]], {a, nn}, {b, a}, {c, b}]; lst1=Sort[lst]; n0=Length[lst]; i=1; Do[If[Part[lst1, t-1]==Part[lst1, t], i=i+1, AppendTo[lst2, i]; i=1], {t, 2, n0}]; lst2

Crossrefs

Cf. A188158, A024153 (distinct side lengths), A051516, A051584, A051585.

Sequence in context: A279620 A278109 A216665 * A258124 A264032 A366597

Adjacent sequences: A301381 A301382 A301383 * A301385 A301386 A301387

Keyword

nonn

Author

Michel Lagneau, Mar 20 2018

Status

approved