Andy Huchala


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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

Knight's Domination 4

n=5

Knight's Domination 5

n=6

Knight's Domination 6

n=7

Knight's Domination 7

n=8

Knight's Domination 8

n=9

Knight's Domination 9

n=10

Knight's Domination 10

n=11

Knight's Domination 11

n=12

Knight's Domination 12

n=13

Knight's Domination 13

n=14

Knight's Domination 14

n=15

Knight's Domination 15

n=16

Knight's Domination 16

n=17

Knight's Domination 17

n=18

Knight's Domination 18

n=19

Knight's Domination 19

n=20

Knight's Domination 20

n=21

Knight's Domination 21

n=22

Knight's Domination 22

n=23

Knight's Domination 23

n=24

Knight's Domination 24

n=25

Knight's Domination 25

n=26

Knight's Domination 26

n=27

Knight's Domination 27

n=28

Knight's Domination 28

n=29

Knight's Domination 29

n=30

Knight's Domination 30

n=31

Knight's Domination 31

n=32

Knight's Domination 32

n=34

Knight's Domination 34

n=36

Knight's Domination 36

n=38

Knight's Domination 38

n=40

Knight's Domination 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."