Neat integer sequences

Interesting thread in which oeis.org/A126140 makes a surprise appearance

A126140(9) = 4 is surprising! There are 1,285 free nonominoes (ignoring rotations and reflections), and 1,050 can tile the plane, but only 41 can tile a rectangle, and two of those are trivial: oeis.org/A126138

A005042: Primes formed by the initial digits of the decimal expansion of Pi oeis.org/A005042

I'm not going to keep going because the next prime that's a prefix of pi is 31415926535897932384626433832795028841

A005042: Primes formed by the initial digits of the decimal expansion of Pi oeis.org/A005042

A006052: Number of magic squares of order n composed of the numbers from 1 to n^2 1, 0, 1, 880, 275305224, 17753889197660635632 oeis.org/A081263

There are many sub-categories of magic squares, like associative (every pair of numbers symmetrically opposite the center sum to the same value) and panmagic (where diagonals that wrap around also sum to the same number as the two standard diagonals)

A006052: Number of magic squares of order n composed of the numbers from 1 to n^2 1, 0, 1, 880, 275305224, 17753889197660635632 oeis.org/A081263

The Luoshu Square, the only solution for n=3, has been certainly known since the 6th century, and possibly hundreds of years longer than that. en.wikipedia.org/wiki/Luoshu_...

A006052: Number of magic squares of order n composed of the numbers from 1 to n^2 1, 0, 1, 880, 275305224, 17753889197660635632 oeis.org/A081263