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A320843 Number of permutations sigma of {1,2,...,n} such that sigma(i) divides i or i divides sigma(i) for 1 <= i <= n. 0
1, 1, 2, 3, 8, 10, 36, 41, 132, 250, 700, 750, 4010, 4237, 10680, 24679, 87328, 90478, 435812, 449586, 1939684, 3853278, 8650900, 8840110, 60035322, 80605209, 177211024, 368759752, 1380348224, 1401414640, 8892787136, 9014369784, 33923638848, 59455553072, 126536289568, 207587882368 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..35.

FORMULA

a(n) = Permanent((x_{ij})) with x_{ij} = 1 if i divides j or j divides i and x_{ij} = 0 otherwise for i,j = 1,...,n. - M. Farrokhi D. G., Dec 30 2018

EXAMPLE

In case n = 4:

permutation

------------

[1, 2, 3, 4]

[1, 4, 3, 2]

[2, 1, 3, 4]

[2, 4, 3, 1]

[3, 2, 1, 4]

[3, 4, 1, 2]

[4, 1, 3, 2]

[4, 2, 3, 1]

PROG

(PARI) a(n) = matpermanent(matrix(n, n, i, j, if (!(i%j) || !(j%i), 1, 0))); \\ Michel Marcus, Dec 30 2018

CROSSREFS

Cf. A005326.

Sequence in context: A107401 A165153 A121989 * A010786 A248822 A005727

Adjacent sequences:  A320840 A320841 A320842 * A320844 A320845 A320846

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Dec 18 2018

EXTENSIONS

a(0), a(24)-a(30) from Alois P. Heinz, Dec 19 2018

a(31)-a(35) from M. Farrokhi D. G., Dec 30 2018

STATUS

approved

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Last modified March 21 10:00 EDT 2019. Contains 321368 sequences. (Running on oeis4.)