cp's OEIS Frontend

A291519 Number of permutations s_1,s_2,...,s_n of 1,2,...,n with s_n = 1 (if n>0) and such that for all j=1,2,...,n, Sum_{i=1..j} s_i divides Sum_{i=1..j} s_i^3.

%I A291519 #29 Aug 26 2017 23:55:26
%S A291519 1,1,1,2,6,18,42,90,228,498,1152,2274,5460,10308,20868,39222,78126,
%T A291519 151092,306144,596796,1204734,2359518,4720854,9229200,18329442,
%U A291519 35889966,71284524,140430234,279790956,554351988,1105988208,2195249184,4371548958,8665192968
%N A291519 Number of permutations s_1,s_2,...,s_n of 1,2,...,n with s_n = 1 (if n>0) and such that for all j=1,2,...,n, Sum_{i=1..j} s_i divides Sum_{i=1..j} s_i^3.
%C A291519 Appears to approximately double (for n > 1) for each successive n. - _Chai Wah Wu_, Aug 26 2017
%H A291519 Chai Wah Wu, <a href="/A291519/b291519.txt">Table of n, a(n) for n = 0..120</a>
%F A291519 A291445(n) >= a(n) + A291518(n) for n > 1.
%e A291519 5                 divides 5^3,
%e A291519 5 + 4             divides 5^3 + 4^3,
%e A291519 5 + 4 + 3         divides 5^3 + 4^3 + 3^3,
%e A291519 5 + 4 + 3 + 2     divides 5^3 + 4^3 + 3^3 + 2^3,
%e A291519 5 + 4 + 3 + 2 + 1 divides 5^3 + 4^3 + 3^3 + 2^3 + 1^3.
%e A291519 So [5, 4, 3, 2, 1] satisfies all the conditions.
%e A291519 -------------------------------------------------------
%e A291519 a(1) = 1: [[1]];
%e A291519 a(2) = 1: [[2, 1]];
%e A291519 a(3) = 2: [[2, 3, 1], [3, 2, 1]];
%e A291519 a(4) = 6: [[2, 3, 4, 1], [2, 4, 3, 1], [3, 2, 4, 1], [3, 4, 2, 1], [4, 2, 3, 1], [4, 3, 2, 1]];
%e A291519 a(5) = 18: [[2, 3, 4, 5, 1], [2, 3, 5, 4, 1], [2, 4, 3, 5, 1], [2, 5, 3, 4, 1], [3, 2, 4, 5, 1], [3, 2, 5, 4, 1], [3, 4, 2, 5, 1], [3, 4, 5, 2, 1], [3, 5, 2, 4, 1], [3, 5, 4, 2, 1], [4, 2, 3, 5, 1], [4, 3, 2, 5, 1], [4, 3, 5, 2, 1], [4, 5, 3, 2, 1], [5, 2, 3, 4, 1], [5, 3, 2, 4, 1], [5, 3, 4, 2, 1], [5, 4, 3, 2, 1]].
%Y A291519 Cf. A291445, A291518.
%K A291519 nonn
%O A291519 0,4
%A A291519 _Seiichi Manyama_, Aug 25 2017
%E A291519 a(0), a(14)-a(33) from _Alois P. Heinz_, Aug 25 2017