cp's OEIS Frontend

A316841 Three-column table read by rows giving integer sides of proper triangles (i,j,k) with i >= j >= k >= 1, j+k > i.

%I A316841 #30 Jul 09 2025 04:47:49
%S A316841 1,1,1,2,2,1,2,2,2,3,2,2,3,3,1,3,3,2,3,3,3,4,3,2,4,3,3,4,4,1,4,4,2,4,
%T A316841 4,3,4,4,4,5,3,3,5,4,2,5,4,3,5,4,4,5,5,1,5,5,2,5,5,3,5,5,4,5,5,5,6,4,
%U A316841 3,6,4,4,6,5,2,6,5,3,6,5,4,6,5,5,6,6,1,6,6,2,6,6,3,6,6,4,6,6,5,6,6,6,7,4,4,7,5,3,7,5,4,7,5,5,7,6,2,7,6,3,7,6,4,7,6,5
%N A316841 Three-column table read by rows giving integer sides of proper triangles (i,j,k) with i >= j >= k >= 1, j+k > i.
%H A316841 Lars Blomberg, <a href="/A316841/b316841.txt">Table of n, a(n) for n = 1..9000</a>
%e A316841 Table begins (imprimitive triples are labeled i):
%e A316841 [1,1,1],
%e A316841 [2,2,1],
%e A316841 [2,2,2],i
%e A316841 [3,2,2],
%e A316841 [3,3,1],
%e A316841 [3,3,2],
%e A316841 [3,3,3],i
%e A316841 [4,3,2],
%e A316841 [4,3,3],
%e A316841 [4,4,1],
%e A316841 [4,4,2],i
%e A316841 [4,4,3],
%e A316841 [4,4,4],i
%e A316841 [5,3,3],
%e A316841 ...
%o A316841 (PARI) for(i=1,6, for(j=1,i, for(k=1,j, if(j+k>i, print1(i,", ",j,", ",k,", "))))) \\ _Hugo Pfoertner_, Jan 25 2020
%Y A316841 There are A002620(k+1) rows that begin with k.
%Y A316841 The three columns are A316843, A316844, A316845.
%Y A316841 A316849 is a compressed version.
%Y A316841 See A316842 for primitive triples.
%Y A316841 See A316851 and A316853 & A317182 for perimeter and area.
%Y A316841 Other related sequences: A051493, A070080, A070081, A070082, A070110.
%K A316841 nonn,look,tabf
%O A316841 1,4
%A A316841 _N. J. A. Sloane_, Jul 23 2018, following a suggestion from _Donald S. McDonald_