User:Pilover819/CartansTriangle

The Cartan's triangle (no Wikipedia article), is the Pascal's triangle's OLDER BROTHER, so to speak. The number on the left is doubled everytime, while the Pascal's triangle is not. The numbers in the Cartan's triangle are related with hypercubes.

The First 10 Rows

                                         1
                                      2     1
                                   4     4     1
                                8     12    6     1
                            16    32     24    8     1
                         32    80     80    40   10     1
                     64    192    240    160   60   12    1
                 128    448    672    560    280   84   14  1
            256     1024   1792  1792   1120   448  112  16  1
        512    2304     4608   5376  4032   2016  672  144 18  1

The Cartan's triangle.

As you see, these are powers of 21 (12 if made backwards), because as you see in Row 1, there is 21. And in the second row, you see 441 which is 21². As you go on, you see two+ digit numbers on the Cartan's triangle. So then you do the same thing to it; carry it down to the number on the left. Here's a link on the Cartan's triangle: Cartan's triangle

• Note: If you have Excel, you will be able to make the Cartan's triangle bigger and bigger.

Here is OEIS on Cartan's Triangle

See also

• Hypercube
• Pascal's triangle
• Simplex
• Cross-polytope
• Exponent
• Microsoft Excel