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.

%I A175134 #17 Jan 29 2025 22:16:51
%S A175134 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,
%T A175134 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,
%U A175134 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
%N 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.
%C A175134 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
%e A175134 For n = 13, suitable pairs of permutations are ((3,2,1),(1,2,3)) and ((3,2,1),(1,3,2)).
%Y A175134 Cf. A014144, A175135, A370369.
%K A175134 nonn
%O A175134 1,5
%A A175134 _Leroy Quet_, Feb 21 2010
%E A175134 Edited and terms a(14) onward added by _Max Alekseyev_, Jan 29 2025.