|
%I #27 Oct 01 2021 19:15:06
%S 2,5,5,10,10,10,17,17,17,17,26,26,26,26,26,37,37,37,37,37,37,50,50,50,
%T 50,50,50,50,65,65,65,65,65,65,65,65,82,82,82,82,82,82,82,82,82,101,
%U 101,101,101,101,101,101,101,101,101
%N Triangle read by rows, formed as the sum of the two versions of the natural numbers filling an equilateral triangle.
%C The natural numbers can sequentially fill a right- or left-handed equilateral triangle. Componentwise addition of the values of these two triangles produces the present triangle.
%C The row sums for this triangle give A034262.
%C The difference between the right- and left-handed triangles produces A049581.
%H Craig Knecht, <a href="/A265129/a265129.jpg">Sum of right and left triangles.</a>
%H Craig Knecht, <a href="/A265129/a265129_1.jpg">Difference between right and left triangles A049581.</a>
%F T(n,k) = n^2 + 1 for k = 1..n and n >= 1. - _Georg Fischer_, Oct 01 2021
%F Sum_{k=1..n} k * T(n,k) = A071237(n). - _Alois P. Heinz_, Oct 01 2021
%e Displayed as a triangle:
%e 2;
%e 5 5;
%e 10 10 10;
%e 17 17 17 17;
%e 26 26 26 26 26;
%e 37 37 37 37 37 37;
%e ...
%p seq(seq(n^2+1,k=1..n),n=1..10); # _Georg Fischer_, Oct 01 2021
%Y Column k=1 gives A002522.
%Y Cf. A049581 (difference of triangles), A034262 (row sum of triangle), A069894 (center column).
%Y Cf. A071237.
%K nonn,tabl
%O 1,1
%A _Craig Knecht_, Dec 02 2015
%E Row 6 with T(6,k)=37 inserted by _Georg Fischer_, Oct 01 2021
|
