A291518 Number of permutations s_1,s_2,...,s_n of 1,2,...,n with s_n = n (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.

1, 1, 1, 2, 6, 12, 30, 78, 186, 414, 912, 2064, 4338, 9798, 20106, 40974, 80196, 158322, 309414, 615558, 1212402, 2417136, 4776654, 9497508, 18726708, 37056150, 72946116, 144230640, 284660874, 564451830, 1118803818, 2224792026, 4420041210, 8791590168

Offset

0,4

Links

Table of n, a(n) for n=0..33.

Formula

a(n+1) = A291445(n).

A291445(n) >= a(n) + A291519(n) for n > 1.

Example

1                 divides 1^3,
1 + 2             divides 1^3 + 2^3,
1 + 2 + 3         divides 1^3 + 2^3 + 3^3,
1 + 2 + 3 + 4     divides 1^3 + 2^3 + 3^3 + 4^3,
1 + 2 + 3 + 4 + 5 divides 1^3 + 2^3 + 3^3 + 4^3 + 5^3.
So [1, 2, 3, 4, 5] satisfies all the conditions.
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a(1) = 1: [[1]];
a(2) = 1: [[1, 2]];
a(3) = 2: [[1, 2, 3], [2, 1, 3]];
a(4) = 6: [[1, 2, 3, 4], [1, 3, 2, 4], [2, 1, 3, 4], [2, 3, 1, 4], [3, 1, 2, 4], [3, 2, 1, 4]];
a(5) = 12: [[1, 2, 3, 4, 5], [1, 3, 2, 4, 5], [2, 1, 3, 4, 5], [2, 3, 1, 4, 5], [2, 3, 4, 1, 5], [2, 4, 3, 1, 5], [3, 1, 2, 4, 5], [3, 2, 1, 4, 5], [3, 2, 4, 1, 5], [3, 4, 2, 1, 5], [4, 2, 3, 1, 5], [4, 3, 2, 1, 5]].

Crossrefs

Cf. A291445, A291519.

Sequence in context: A335711 A032177 A095349 * A291445 A320664 A022916

Adjacent sequences: A291515 A291516 A291517 * A291519 A291520 A291521

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2017

Status

approved