The centred square numbers

Rule

Each term is: Two times the number squared minus two times the number plus one

Known as: The centred square numbers

Each number is the sum of two consecutive squares, as illustrated above.

The first 50 terms (starting from n=1) are:

1 5 13 25 41 61 85 113 145 181 221 265 313 365 421 481 545 613 685 761 841 925 1013 1105 1201 1301 1405 1513 1625 1741 1861 1985 2113 2245 2381 2521 2665 2813 2965 3121 3281 3445 3613 3785 3961 4141 4325 4513 4705 4901

Example

To get the value for n=11:

• Take 2 times the number squared, giving 242
• Subtract 2 times the number, giving 220
• Add 1, giving 221

So the result is 221.