cp's OEIS Frontend

A265129 Triangle read by rows, formed as the sum of the two versions of the natural numbers filling an equilateral triangle.

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