|
| |
|
|
A118705
|
|
a(n) = determinant of n X n circulant matrix whose first row is the first n triangular numbers A000217(0), A000217(1), ... A000217(n-1).
|
|
1
| | |
|
|
|
OFFSET
| 1,3
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Circulant Matrix.
|
|
|
FORMULA
| a(n) = (-1)^(n-1)*n^(n-2)*(n+1)*(n-1)*((n+1)^n-(n-1)^n)/(6*2^n) [From Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 03 2010]
|
|
|
EXAMPLE
| a(2) = - 1 because of the determinant -1 =
| 0, 1 |
| 1, 0 |.
a(4) = -1360 = determinant
|0,1,3,6|
|6,0,1,3|
|3,6,0,1|
|1,3,6,0|.
|
|
|
CROSSREFS
| See also: A048954 Wendt determinant of n-th circulant matrix C(n). A052182 Circulant of natural numbers. A066933 Circulant of prime numbers. A086459 Circulant of powers of 2.
Cf. A000045, A048954, A052182, A066933, A086459, A086569.
Sequence in context: A092705 A061321 A091993 * A013926 A110696 A007222
Adjacent sequences: A118702 A118703 A118704 * A118706 A118707 A118708
|
|
|
KEYWORD
| easy,sign
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 20 2006
|
| |
|
|
