A265129 - OEIS

A265129

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

2, 5, 5, 10, 10, 10, 17, 17, 17, 17, 26, 26, 26, 26, 26, 37, 37, 37, 37, 37, 37, 50, 50, 50, 50, 50, 50, 50, 65, 65, 65, 65, 65, 65, 65, 65, 82, 82, 82, 82, 82, 82, 82, 82, 82, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101

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OFFSET

1,1

COMMENTS

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.

The row sums for this triangle give A034262.

The difference between the right- and left-handed triangles produces A049581.

LINKS

Table of n, a(n) for n=1..55.

Craig Knecht, Sum of right and left triangles.

Craig Knecht, Difference between right and left triangles A049581.

FORMULA

T(n,k) = n^2 + 1 for k = 1..n and n >= 1. - Georg Fischer, Oct 01 2021

Sum_{k=1..n} k * T(n,k) = A071237(n). - Alois P. Heinz, Oct 01 2021

EXAMPLE

Displayed as a triangle:

5 5;