Andy Huchala

Home

The Online Encyclopedia of Integer Sequences is an online database of integer-valued sequences that anyone can contribute to. It's got a lot of interesting problem statements, many with only partial solutions. I've compiled a short list of problems I've been interested in, with graphics included if possible.

A261752 (Knight's Domination): "Minimum number of knights on an n X n chessboard such that every square is attacked."

Examples of optimal tilings:

n=4

n=5

n=6

n=7

n=8

n=9

n=10

n=11

n=12

n=13

n=14

n=15

n=16

n=17

n=18

n=19

n=20

n=21

n=22

n=23

n=24

n=25

n=26

n=27

n=28

n=29

n=30

n=31

n=32

n=34

n=36

n=38

n=40

A004670 (and friends): "Theta series of Barnes-Wall lattices in dimension 2^n."

Dimension (OEIS)

Theta Series plot:

Theta Series 4

Theta Series 8

Theta Series 16

Theta Series 32

Theta Series 64

Other OEIS Problems I Find Interesting But Don't Have Any Graphics For

A181746: "List of dimensions for which there exist several non-isomorphic irreducible representations of E8.."

A343266 (proposed): "List of dimensions for which there exist 8 or more non-isomorphic irreducible representations of E6."