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# Sequences

#### ASM Number

Returns the number of alternating sign matrices of the given order.
 int asm_number (int n)

#### ASM Triangle Row

Returns a row of the alternating sign matrix triangle.
 std::vector asm_triangle_row (int n)

#### Catalan Numbers List

Computes the Catalan numbers, of order 0 to n.
 std::vector catalan_numbers_list (int n)

#### Catalan Triangle Row

Computes the row of the given order in Catalan's triangle.
 std::vector catalan_triangle_row (int n, bool first = true)

#### Derangements List

Returns the number of derangements of 0 through \e n objects.
 std::vector derangements_list (int n)

#### Derangements Number

Calculates the number of derangements of \e n objects.
 int derangements_number (int n)

#### Euler Triangle Row

Computes the row of order \e n in the Euler triangle.
 std::vector euler_triangle_row (int n)

#### Involution Numbers List

Calculates the numbers of involutions of 0 through \e n objects.
 std::vector involution_numbers_list (int n)

#### Morse Thue Number

Calculates the Morse-Thue number of the given order.
 int morse_thue_number (int n)

Calculates the Padovan numbers of orders 0 through \e n.

#### Pentagonal Number

Calculates the pentagonal number of the given order.
 int pentagonal_number (int n)[inline]

#### Perrin Numbers List

Computes the first \e n values of a Perrin sequence.
 std::vector perrin_numbers_list (int n)

#### Schroeder Numbers List

Computes the first \e n values of the Schroeder sequence.
 std::vector schroeder_numbers_list (int n)

#### Young Number

Calculates the Young tableau number of the given order.
 int young_number (int n)

#### Bell Numbers List

Returns the Bell numbers of order 0 to n.
 std::vector bell_numbers_list (int n)

#### Fixed Permutation

Calculates the number of permutations of \e n objects with \e m fixed.
 int fixed_permutation (int n, int m)