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Let H_n denote the nth hexagonal number and S_m the mth square number, then a number which is both hexagonal and square satisfies the equation H_n=S_m, or n(2n-1)=m^2. (1) ...

A number which is simultaneously octagonal and square. Let O_n denote the nth octagonal number and S_m the mth square number, then a number which is both octagonal and square ...

In a normal n×n Latin square, the entries in each row and column are chosen from a "global" set of n objects. Like a Latin square, a partial Latin square has no two rows or ...

[scale=.3]/troves/MathOzTeX/graphics/gifs/melencol.jpg Dürer's magic square is a magic square with magic constant 34 used in an engraving entitled Melencolia I by Albrecht ...

The equilateral elongated square dipyramid, illustrated above together with its net, is Johnson solid J_(15). A version of the elongated square dipyramid that is "squashed" ...

In 1750, Benjamin Franklin constructed the above 8×8 semimagic square having magic constant 260. Any half-row or half-column in this square totals 130, and the four corners ...

Johnson solid J_(23).

A number which is simultaneously a pentagonal number P_n and a square number S_m. Such numbers exist when 1/2n(3n-1)=m^2. (1) Completing the square gives ...

Combine the two above squares on the left into the single large square on the right.

Stern's diatomic series is the sequence 1, 1,2, 1,3,2,3, 1,4,3,5,2,5,3,4, (1) ... (OEIS A002487) which arises in the Calkin-Wilf tree. It is sometimes also known as the fusc ...