Sum of first 4 powers

Rule

Each term is: The number cubed, plus n squared, plus n, plus one

Known as: Sum of first 4 powers

The sum of the first four powers of n.

The first 50 terms (starting from n=0) are:

1 4 15 40 85 156 259 400 585 820 1111 1464 1885 2380 2955 3616 4369 5220 6175 7240 8421 9724 11155 12720 14425 16276 18279 20440 22765 25260 27931 30784 33825 37060 40495 44136 47989 52060 56355 60880 65641 70644 75895 81400 87165 93196 99499 106080 112945 120100

Example

To get the value for n=13:

• Cube the number, giving 2197.
• Add the original number squared, giving 2366.
• Add the original number, giving 2379.
• Add one, giving 2380.

So the result is 2380.