A175135 -id:A175135 - cp's OEIS frontend

A175134 a(n) = number of pairs of permutations (p, q) of the same (arbitrary) size m such that f_m(f_{m-1}(...f_1(1)...)) = n, where f_i(x) = p_i*x + q_i.

1, 1, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 2, 4, 4, 4, 2, 4, 1, 3, 1, 2, 2, 1, 1, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 6, 4, 8, 6, 8, 6, 8, 6, 16, 12, 14, 6, 12, 10, 16, 18, 14, 14, 10, 10, 10, 14, 12, 10, 10, 8, 4, 13, 15, 4, 13, 6, 8, 6, 8, 2, 11, 6, 5, 7, 2, 11, 7, 6, 6, 5, 3, 6, 6, 2, 5, 2, 4, 3, 4, 3, 3, 1, 3, 5, 5, 1, 2, 3, 2, 0, 3, 2, 2, 3, 3, 4, 4, 3, 4, 2, 0, 2, 3, 2, 0, 1, 3, 2, 3, 1, 1, 1, 0, 1, 4, 2, 2, 1, 4, 1, 2, 0, 2, 3, 6, 0, 1, 1, 0, 1, 3, 3, 2, 0, 2, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0

Offset: 1

Leroy Quet, Feb 21 2010

nonn

For a fixed m, the smallest value of f_m(f_{m-1}(...f_1(1)...)) is achieved on the pair ((m,m-1,...,1), (1,2,...,m)) and is given by A370369(m) + m = A014144(m) + m!. Hence, to compute a(n) one can restrict m to those satisfying A014144(m) + m! <= n. - Max Alekseyev, Jan 29 2025

			For n = 13, suitable pairs of permutations are ((3,2,1),(1,2,3)) and ((3,2,1),(1,3,2)).

Cf. A014144, A175135, A370369.

Edited and terms a(14) onward added by Max Alekseyev, Jan 29 2025.

cp's OEIS Frontend

A175134 a(n) = number of pairs of permutations (p, q) of the same (arbitrary) size m such that f_m(f_{m-1}(...f_1(1)...)) = n, where f_i(x) = p_i*x + q_i.

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