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.

1, 1, 1, 2, 6, 18, 42, 90, 228, 498, 1152, 2274, 5460, 10308, 20868, 39222, 78126, 151092, 306144, 596796, 1204734, 2359518, 4720854, 9229200, 18329442, 35889966, 71284524, 140430234, 279790956, 554351988, 1105988208, 2195249184, 4371548958, 8665192968

Offset

0,4

Comments

Appears to approximately double (for n > 1) for each successive n. - Chai Wah Wu, Aug 26 2017

Links

Chai Wah Wu, Table of n, a(n) for n = 0..120

Formula

A291445(n) >= a(n) + A291518(n) for n > 1.

Example

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

Crossrefs

Cf. A291445, A291518.

Sequence in context: A364672 A014741 A016059 * A027556 A195584 A225316

Adjacent sequences: A291516 A291517 A291518 * A291520 A291521 A291522

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2017

Extensions

a(0), a(14)-a(33) from Alois P. Heinz, Aug 25 2017

Status

approved