The Catalan numbers give the number of ways to tile an n-sized stair case with exactly n rectangles.

The Catalan numbers give the number of ways to tile an n-sized stair case with exactly n rectangles.

Catalan number 4x4 grid example.svg

Catalan number 4x4 grid example.svg

910 is the generalized Catalan number C(11,4).

910 is the generalized Catalan number C(11,4).

An Introduction to Catalan Numbers ( Compact Textbooks in Mathematics) (Hardcover)

An Introduction to Catalan Numbers ( Compact Textbooks in Mathematics) (Hardcover)

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Catalan Numbers

Catalan Numbers (Paperback)

 Cn (the nth Catalan number) is, among other things, the number of monotonic paths along the edges of a grid with n × n square cells, which do not pass above the diagonal. A monotonic path is one which starts in the lower left corner, finishes in the upper right corner, and consists entirely of edges pointing rightwards or upwards. The diagrams show the case for n = 4:

Cn (the nth Catalan number) is, among other things, the number of monotonic paths along the edges of a grid with n × n square cells, which do not pass above the diagonal. A monotonic path is one which starts in the lower left corner, finishes in the upper right corner, and consists entirely of edges pointing rightwards or upwards. The diagrams show the case for n = 4:

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