A frieze pattern consists of repeated copies of a single motif.
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Conway and Guy (1996) define a frieze pattern as an arrangement of numbers at the intersection of two sets of perpendicular diagonals such that 
(for an additive frieze pattern) or 
(for a multiplicative frieze pattern) in each diamond.
In the positive-integral multiplicative case bounded by two rows of 1s, an admissible diagonal determines the frieze once its horizontal position and direction are fixed.
For integer 
, the number of such diagonals across all friezes with
rows, including both bounding rows,
is the Catalan number 
(Conway and Guy 1996, pp. 96-106; Stanley 1999, pp. 231
and 269).
