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Name, Anumber (Credits) 
Brief Description 
Pictures 

Peaceable Queens:
A250000
(SmithPetrieGent)

Place k white queens, k black queens on n X n board so they don't attack each other.
Fig. shows 11X11 board, where k=17 is maximal, illustrating A250000(11) = 17.
Only 13 terms are known.



Peaceable Queens (continued):
A250000
(Michael De Vlieger)

"Peace to the Max" Tshirt showing maximal nonattacking arrangement of 17 black queens and 17 white queens on 11X11 board, illustrating A250000(11) = 17.



The toothpick sequence:
A139250
(ApplegatePolSloane)

Fig. shows structure after 23 generations, when there are 283 toothpicks, illustrating
A139250(23) = 283.



Toothpick sequence (cont.):
A139250
(Michael De Vlieger)

Tshirt designs from Michael De Vlieger.
Fig. on left shows structure after 28 generations, when there are 423 toothpicks, illustrating
A139250(28) = 423.



Eshaped toothpicks:
A161330
(Omar Pol, D. Applegate)

Fig. shows structure after 32 generations, when there are 1124 Etoothpicks, illustrating
A161330(32) = 1124.



More toothpick structures:
For a very large number of similar structures, both pictures and animations, see David Applegate's Toothpick Movie Page

Fig. shows gullwing toothpick structure after 16 generations, illustrating
A187220(16)=32.

For thousands of similar pictures, see the Toothpick Movie Page
Click "pdf" button to save the pictures.


Fredkin's Replicator:
A160239
(N. J. A. Sloane, Mathematica)

Number of ON cells after n generations in Fredkin's Replicator.
After 15 generations there are 416 ON cells, so
A160239(15) = 416,



Fastestgrowing OddRule CA:
A255462
(N. J. A. Sloane, Mathematica)

Number of ON cells after n generations in OddRule Cellular Automaton 365.
After 15 generations there are 606 ON cells, so
A255462(15) = 606.



Square grid with no red square:
A227133
(Giovanni Resta)

Maximal number of points in nXn grid such that no 4 form a square. Figure shows 41 red points in 8 X 8 grid such that no 4 red points form a square,
illustrating A227133(8) = 41.
Only 10 terms are known.



A corner design:
A232467
(Craig S. Kaplan)

A (20,2) corner design of C. S. Kaplan (Bridges, 2013), "redrawn from the menu
of Os Tibetanos, a Tibetan restaurant in Lisbon".



Circles in the plane:
A250001
(N. J. A. Sloane)

Number of ways to draw n circles in the plane.
Shows 7 of the 14 ways to draw 3 circles,
partly illustrating A250001(3) = 14.
Only 5 terms are known.



Meanders in nXn grid:
A200000
(Jonathan Wild)

There are 42 different meanders in a 5X5 grid, so
A200000(5) = 42.



Coloring empires:
A230628
(Ian Stewart)

Each empire has n countries: how many colors are needed? n=1 is 4color problem.
Figure shows case n=2 which requires 12 colors, illustrating
A230628(2) = 12.



Dissecting polygon to square:
A110312
(V. Vaishampayan)

Minimal number of pieces for dissecting an ngon into a square.
Conjecturally, 4 pieces are needed for the triangle to square problem,
so A110312(3) = 4 (?).



Kobon triangles:
A006066
(Johannes Bader)

Maximal number of triangles formed from n lines drawn in the plane.
Figure shows optimal arrangement of 17 lines, giving 85 triangles,
illustrating A006066(17) = 85.
Only 9 terms are known.



Packing points in a triangle:
A243487
(Robert Israel)

Largest minimal Manhattan distance for n points in a simplex:
Figure shows optimal arrangement of 17 points,
illustrating A243487(17) / A243576(17) = 6/13.



Min number of pieces
in dissection of polygon:
A160860
(Vladimir Letsko)

Min number of pieces in convex ngon with all diagonals drawn.
For heptagon, 47 pieces is minimal: A160860(7) = 47.
Only known for n<9.



Figurate numbers (1):
A169721
(Alice V. Kleeva)

Geometrical design based on the figurate numbers of Pythagoras and on the regular division of the plane by the square grid.



Figurate numbers (2):
A169727
(Alice V. Kleeva)

Geometrical design based on the figurate numbers of Pythagoras and on a regular division of the plane into a grid of hexagons and squares.



Coordination sequence
for 3.3.3.3.6 tiling:
A250120
(Darrah Chavey)

Number of points at distance n
from origin in planar net 3.3.3.3.6.



Isolated semiprimes:
A113688
(Alois Heinz)

Spiral showing all semiprimes ≤ 10000, with isolated semiprimes in red.



Selfgenerating sequence avoiding arithmetic progression:
A229037
(J. W. Grahl, X. Gregg)

a(n) is as small as possible such that no three terms a(j), a(j+k), a(j+2k) form an arithmetic progression.
Graph of 10000 terms.



Spacefilling curve of order 3:
A265671
(Joerg Arndt)

Third stage of a spacefilling curve.
This is a single curve (with color added).



Noncrossing partitions:
A000108
(Tilman Piesk)

Among other things, the Catalan numbers count noncrossing partitions.
Figure shows the 42 noncrossing partitions on five points: A000108(5) = 42.



Somos6 surface:
A006722
(FedorovHone)

Projection of 4dimensional surface defined by Somos6 sequence.

