A118712 a(n) = Determinant of n X n circulant matrix whose first row is A000001(1), A000001(2), ..., A000001(n) where A000001(n) = number of groups of order n.

1, 0, 0, -5, 6, -16, 9, -134400, 647248, -1711908, 6076067, -85248000, 116477425, -1764364437, 909276004, -522319050599375232, 14313181351994538493, -165893335414907083200, 2939566160282258664451, -5007637771411479278976, 75399747694572065660672

Offset

1,4

Links

Table of n, a(n) for n=1..21.

Eric Weisstein's World of Mathematics, Circulant Matrix.

Example

a(4) = -5 because of the determinant -5 =
|1,1,1,2|
|2,1,1,1|
|1,2,1,1|
|1,1,2,1|.
a(11) = 6076067 = determinant
|1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1|
|1, 1, 1, 1, 2, 1, 2, 1, 5, 2, 2|
|2, 1, 1, 1, 1, 2, 1, 2, 1, 5, 2|
|2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 5|
|5, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1|
|1, 5, 2, 2, 1, 1, 1, 1, 2, 1, 2|
|2, 1, 5, 2, 2, 1, 1, 1, 1, 2, 1|
|1, 2, 1, 5, 2, 2, 1, 1, 1, 1, 2|
|2, 1, 2, 1, 5, 2, 2, 1, 1, 1, 1|
|1, 2, 1, 2, 1, 5, 2, 2, 1, 1, 1|
|1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 1|.

Prog

(GAP) A118712 := n -> DeterminantMat(List([0..n-1], i->List([0..n-1], j->NrSmallGroups(((j-i) mod n)+1)))); # Eric M. Schmidt, Nov 17 2013

Crossrefs

Cf. A000001, A048954, A052182, A066933, A086459, A086569.

Sequence in context: A019071 A028285 A007430 * A130878 A104422 A026547

Adjacent sequences: A118709 A118710 A118711 * A118713 A118714 A118715

Keyword

sign

Author

Jonathan Vos Post, May 20 2006

Extensions

a(1) corrected by and more terms from Eric M. Schmidt, Nov 17 2013

Status

approved